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Minisymposia Abstracts

IndexA

Absil, Pierre-Antoine, 44Acar, Evrim, 35Agullo, Emmanuel, 34, 46Ahuja, Kapil, 36, 40Aishima, Kensuke, 45Akian, Marianne, 48Alastair Spence, Alastair, 51Ali, Murtaza, 32Allamigeon, Xavier, 54Amat, Sergio, 62Amestoy, Patrick, 60Amodei, Luca, 64Amsallem, David, 10Antoine, Xavier, 19Antoulas, A.C., 38Arioli, Mario, 31, 40, 53Ashcraft, Cleve, 60Asif, M. Salman, 48Aurentz, Jared L., 59Avron, Haim, 16Axelsson, Owe, 12

BBaboulin, Marc, 12, 16Bai, Zhong-Zhi, 20Bailey, David H., 60Ballard, Grey, 22, 29Barioli, Francesco, 28Barlow, Jesse, 32Barreras, Álvaro, 9Barrett, Wayne, 28Barrio, Roberto, 60, 61Beattie, Christopher, 13, 38, 41Bebiano, Natália, 14Becker, Dulceneia, 12, 16Becker, Stephen, 48Beckermann, Bernhard, 13Ben-Ari, Iddo, 19Bendito, Enrique, 14, 61Benner, Peter, 17, 36, 37Benning, Martin, 54Bergamaschi, Luca, 53Berman, Abraham, 28Beyer, Lucas, 32Bientinesi, Paolo, 32Bini, Dario A., 8Bioucas-Dias, Jose, 50Bı́yı́koğlu, Türker, 61Blank, Luise, 27Bognet, Brice, 21Boiteau, Olivier, 60

Boito, Paola, 58Bolten, Matthias, 9Boman, Erik G., 34Börm, Steffen, 51Borwein, Jonathan M., 60Bouhamidi, Abderrahman, 24Boutsidis, Christos, 13Boyanova, Petia, 12Božović, Nemanja, 39Brannick, James, 26Brauchart, Johann S., 64Breiten, Tobias, 17Bro, Rasmus, 35Bru, Rafael, 47Brualdi, Richard A., 21Buchot, Jean-Marie, 64Budko, Neil, 19Bueno, Maria I., 59Buluç, Aydın, 29Busquier, S., 62Butkovič, Peter, 55Buttari, Alfredo, 60Byckling, Mikko, 19

CCai, Xiao-Chuan, 40Calvin, Christophe, 45Campos, Carmen, 52Candès, Emmanuel, 48, 54Candela, Vicente F., 28, 62, 63Cantó, Rafael, 9Carden, Russell L., 41, 55Carmona, Ángeles, 14, 61Carson, Erin, 29, 30Castro González, Nieves, 36Catral, Minerva, 9Cerdán, Juana, 53Chan, Raymond H., 56Chang, Xiao-Wen, 32Chaturantabut, Saifon, 13Chen, Jie, 24Chiang, Chun-Yueh, 42Chinesta, Francisco, 21Chitour, Yacine, 15Chow, Edmond, 31Chu, Delin, 42Chu, Eric King-wah, 39, 39Chu, Moody T., 39Cornelio, Anastasia, 30Cvetković-Ilić, Dragana S., 36

DDachsel, Holger, 43

2

3 2012 SIAM Conference on Applied Linear Algebra

Dahl, Geir, 21Damm, Tobias, 64Dandouna, Makarem, 45, 46de Hoop, Maarten V., 58, 58, 60de la Puente, Marı́a Jesús, 54De Lathauwer, Lieven, 35De Sterck, Hans, 35de Sturler, Eric, 11, 13, 36, 40De Terán, Fernando, 59, 59De Vlieger, Jeroen, 56Deadman, Edvin, 8Demmel, James W., 22, 23, 29, 30Derevyagin, Maxim, 17Dhillon, Inderjit S., 24Di Benedetto, Maria Domenica, 14Diao, Huaian, 33, 43Djordjevi, Dragan S., 36Dolean, Victorita, 34Donatelli, Marco, 9, 30Dongarra, Jack, 12, 16, 46Dopico, Froilán M., 37, 37, 49, 59Drineas, Petros, 13Drmač, Zlatko, 41Druinsky, Alex, 22, 60Drummond, L. A. (Tony), 46, 52Druskin, Vladimir, 13, 17Du, Xiuhong, 26Dubois, Jérôme, 45Duff, Iain S., 31, 31, 34Dunlavy, Daniel M., 35

EEffenberger, Cedric, 33Eidelman, Yuli, 52, 58Elman, Howard, 51Emad, Nahid, 45, 46Embree, Mark, 18, 55Encinas, Andrés M., 14, 61Erhel, Jocelyne, 53Erway, Jennifer B., 50, 56Ezzatti, Pablo, 32

FFabregat-Traver, Diego, 32Fadili, Jalal, 48Falcó, Antonio, 22, 29Falgout, Robert D., 11Fallat, Shaun M., 28, 28Farber, Miriam, 21Farhat, Charbel, 10Faverge, Mathieu, 46Feng, Lihong, 37Ferreira, Carla, 49Ferronato, Massimiliano, 47Fezzani, Riadh, 26Figueiredo, Mario, 50

Filar, Jerzy, 19Fornasini, Ettore, 15Freitag, Melina A., 51Fuenmayor, F. Javier, 21Furtado, Susana, 14Futamura, Yasunori, 45

GGalántai, Aurél, 46Gaubert, Stéphane, 48, 54Gavalec, Martin, 49, 55Gemignani, Luca, 58Geuzaine, Christophe, 19Ghandchi Tehrani, Maryam, 57Ghnatios, Chady, 21Ghysels, Pieter, 29Gillis, Nicolas, 50Giner, Eugenio, 21Giraldi, Loic, 29Giraud, Luc, 34, 46Gohberg, Israel, 58Goldberg, Felix, 28Goldfarb, Donald, 54Goubault, Eric, 54Gracia, Juan-Miguel, 49Gräf, Manuel, 65Grant, Michael, 48Grasedyck, Lars, 64Gratton, Serge, 27Greengard, Leslie, 52Greif, Chen, 15, 16Grigori, Laura, 23, 26, 29Grimes, Roger, 60Gu, Ming, 23Guermouche, Abdou, 34, 46Guerrero, Johana, 56Gugercin, Serkan, 11, 13, 36, 38, 41Guglielmi, Nicola, 10, 55, 57Guivarch, Roman, 34Guo, Chun-Hua, 63Gürbüzbalaban, Mert, 55Gutiérrez, José M., 62Gutiérrez-Gutiérrez, Jesús, 18Güttel, Stefan, 13

HHached, Mustapha, 24Hackbusch, Wolfgang, 29Hall, H. Tracy, 28Han, Lixing, 9Hanke, Martin, 30Hartwig, R., 43Hauret, Patrice, 34Havé, Pascal, 25Hayami, Ken, 33Hein, Matthias, 24

2012 SIAM Conference on Applied Linear Algebra 4

Heinecke, Alexander, 44Heins, Pia, 54Henson, Van Emden, 11Herault, Thomas, 46Hernández, Araceli, 42Heroux, Michael A., 34Herzog, Roland, 27Heuveline, Vincent, 31Higham, Nicholas J., 8, 38Hilario, Lucı́a, 22Ho, Kenneth L., 52Hogben, Leslie, 28Holodnak, John T., 40Holtz, Olga, 22Hsieh, Cho-Jui, 24Hu, Xiaofei, 50Huang, Tsung-Ming, 42Huckle, Thomas, 9, 47Huhs, Georg, 45Huhtanen, Marko, 19Humet, Matthias, 52Hunter, Jeffrey J., 19

IIannazzo, Bruno, 8Igual, Francisco D., 32Ipsen, Ilse C. F., 12, 40Ishteva, Mariya, 44

JJanna, Carlo, 47Jarlebring, Elias, 33, 64Jbilou, Khalide, 23, 24Jeuris, Ben, 44Jiang, Hao, 61Jiménez, Adrián, 54Jiranek, Pavel, 27Johnson, Charles R., 14Jokar, Sadegh, 38Jönsthövel, Tom, 47Joshi, Shantanu H., 56

KKabadshow, Ivo, 43Kahl, Karsten, 26Kambites, Mark, 49Karimi, Sahar, 54Karow, Michael, 49Katz, Ricardo D., 54Kaya, Oguz, 31Khabou, Amal, 23Khan, Mohammad Kazim, 30Kılıç, Mustafa, 55Kilmer, Misha E., 13Kirkland, Steve, 20Knight, Nicholas, 29, 30

Kolda, Tamara G., 35Kollmann, Markus, 20Kopal, Jiřı́, 37Koutis, Ioannis, 16Kraus, Johannes, 11Krendl, Wolfgang, 20Kressner, Daniel, 39, 56Kronbichler, Martin, 12Kunis, Susanne, 43Kuo, Chun-Hung, 39Kuo, Yueh-Cheng, 42

LL’Excellent, Jean-Yves, 60Landi, Germana, 50Langguth, Johannes, 31Langou, Julien, 46Latouche, Guy, 63Lattanzi, Marina, 42Laub, Alan J., 13Lecomte, Christophe, 57Legrain, Gregory, 29Leydold, Josef, 61Leygue, Adrien, 21Li, Ren-Cang, 63Li, Tiexiang, 39, 39Li, Xiaoye S., 58, 60Liesen, Jörg, 11Lim, Lek-Heng, 40Lim, Yongdo, 44Lin, Matthew M., 39, 42Lin, Wen-Wei, 39, 42Lipshitz, Benjamin, 22Litvinenko, Alexander, 22Lorenz, Dirk, 48Lubich, Christian, 10Lucas, Bob, 60Luce, Robert, 31Lukarski, Dimitar, 31

MMa, Shiqian, 54Mach, Susann, 27Mackey, D. Steven, 59, 59Maeda, Yasuyuki, 45Magdon-Ismail, Malik, 13Magreñán, A., 62Mahoney, Michael W., 16, 24Manguoğlu, Murat, 25Marcia, Roummel F., 56Marek, Ivo, 20Marı́n, José, 47, 53Marques, Osni, 52Marquina, Antonio, 56Martin, David, 17Martin-Dorel, Érik, 61


Martı́nez, Ángeles, 53Mas, José, 47, 53Mason, Paolo, 15Masson, Roland, 25Matthies, Hermann G., 22Mayo, Jackson R., 35McNally, Arielle Grim, 40Meerbergen, Karl, 16, 33, 51, 56Mehrmann, Volker, 38Melquiond, Guillaume, 61Meng, Xiangrui, 24Mengi, Emre, 55Michiels, Wim, 16, 33, 57, 64Miedlar, Agnieszka, 40Miller, Gary, 16Miller, Killian, 35Milzarek, Andre, 48Ming, Li, 40Mitjana, Margarida, 14, 61Möller, Michael, 54Montés, Nicolás, 22Mora, Marta C., 22Moreira Cardoso, Domingos, 21Morigi, Serena, 30Morikuni, Keiichi, 33Moro, Julio, 49Mosić, D., 36Moulding, Erin, 16Muhič, Andrej, 51Muller, Jean-Michel, 61

NNagy, James G., 30Nakata, Maho, 46Nakatsukasa, Yuji, 8, 34, 38, 45Napov, Artem, 58Nataf, Frédéric, 25, 26, 34Neumann, Michael, 9Newton, Chris, 12Neytcheva, Maya, 12Ng, Esmond, G., 31Ng, Michael K., 50Nguyen, Giang T., 63Niknejad, Amir, 18Noschese, Silvia, 23Noutsos, Dimitrios, 9Nouy, Anthony, 21, 29Nuentsa Wakam, Désiré, 53

OOgita, Takeshi, 46Oishi, Shin’ichi, 45Okoudjou, Kasso, 65Olshevsky, Vadim, 37Orban, Dominique, 16Osher, Stanley J., 56

Overton, Michael L., 55

PPaige, Chris, 40Pajonk, Oliver, 22Pan, Victor, 57Papathanasiou, Nikolaos, 9Parlett, Beresford, 49Patrı́cio, Pedro, 43Pauca, Paul, 50Pearson, John, 20, 27Pechstein, Clemens, 34Pedregal, P., 62Peláez, Marı́a J., 9, 49Peled, Inon, 22Peng, Richard, 16Peña, Juan Manuel, 9Peris, Rosa M., 63Pestana, Jennifer, 15, 15Petiton, Serge G., 45PETSc Team, 46Pfetsch, Marc, 48Pflüger, Dirk, 44Piccolomini, Elena Loli, 30, 50Pinheiro, Eduardo, 18Pini, Giorgio, 47Pippig, Michael, 43Plávka, Ján, 55Plemmons, Robert J., 9, 50Plestenjak, Bor, 51Polizzi, Eric, 25Poloni, Federico, 41Popescu, Radu, 34Poulson, Jack, 53Prasad, Sudhakar, 50Providência, J. da, 14Psarrakos, Panayiotis, 9

QQuraischi, Sarosh, 38

RRajamanickam, Siva, 34Ralha, Rui, 8Ramage, Alison, 12Ramaswami, V., 63Ramlau, Ronny, 30Rantzer, Anders, 38Raydan, Marcos, 56Rees, Tyrone, 15Reichel, Lothar, 17, 23, 30Reis, Timo, 41Remis, Rob, 13Robert, Yves, 46Ródenas, Juan José, 21Rohwedder, Thorsten, 10


Rojas, Marielba, 56Roman, Jean, 34, 46Roman, Jose E., 52Romberg, Justin, 48Romero Sánchez, Pantaleón David, 28, 62Rosić, Bojana, 22Rozložnı́k, Miroslav, 37Ruiz, Daniel, 34Rump, Siegfried M. , 61

SSaad, Yousef, 26Saak, Jens, 64Sachs, Ekkehard, 27Sadok, Hassane, 23Saied, Faisal, 25Sakurai, Tetsuya, 45Sameh, Ahmed H., 25Sanders, Geoffrey D., 11Sarbu, Lavinia, 27Sarkis, Marcus, 26Saunders, M. A., 24Scarpa, Giannicola, 28Schaerer, Christian E., 26Scheichl, Robert, 34Scheinberg, Katya, 54Schenk, Olaf, 25Schröder, Christian, 51Schroder, Jacob B., 11Schwartz, Oded, 22, 22, 29Sciriha, Irene, 21Scott, Jennifer, 53Sedlacek, Matous, 47Sergeev, Sergeı̆, 49Serra Capizzano, Stefano, 8Serrano, Sergio, 60Severini, Simone, 28Sgallari, Fiorella, 30Shader, Bryan, 28Sharify, Meisam, 48Shieh, Shih-Feng, 42Sifuentes, Josef, 18Sigalotti, Mario, 15Simić, Slobodan K., 62Simoncini, Valeria, 17, 20Smith, Barry, 46Smoktunowicz, Alicja, 37Solomonik, Edgar, 23Sonneveld, Peter, 26Soodhalter, Kirk M., 37Sootla, Aivar, 38Sorber, Laurent, 35Sorensen, D.C., 41Sou, Kin Cheong, 38Spence, Alastair, 51

Spillane, Nicole, 34Stevanović, Dragan, 62Stoll, Martin, 27, 27Štovı́ček, Pavel, 17Strakoš, Zdeněk, 11Stykel, Tatjana, 41Sun, Hai-Wei, 8Szydlarski, Mikolaj, 25Szyld, Daniel B., 15, 26, 36, 37

TTang, Ping Tak Peter, 25Taslaman, Leo, 34Thome, Néstor, 42Thornquist, Heidi, 53Tillmann, Andreas, 48Tisseur, Françoise, 34, 59Titley-Peloquin, David, 27Tobler, Christine, 39Toledo, Sivan, 16, 22, 60Tomov, Stanimire, 12Tran, John, 60Treister, Eran, 10Trenn, Stephan, 15Tůma, Miroslav, 37, 47Tyaglov, Mikhail, 14

UUçar, Bora, 31Ulbrich, Michael, 48Urbano, Ana M., 9Urquiza, Fabián, 42Uschmajew, André, 10, 44

VValcher, Maria Elena, 15Van Barel, Marc, 35, 52Van Beeumen, Roel, 16van de Geijn, Robert A., 32van den Berg, Ewout, 54van den Driessche, P., 28van der Holst, Hein, 28Van Dooren, Paul, 44van Gijzen, Martin B., 36, 47Van Houdt, Benny, 63Vandebril, Raf, 18, 44, 59Vandereycken, Bart, 44, 44Vanroose, Wim, 29Varona, J. L., 62Vassalos, Paris, 9Vassilevski, Panayot S., 11Vavasis, Stephen, 54Voss, Heinrich, 33Vuik, Kees, 47


WWagenbreth, Gene, 60Wang, Shen, 58, 60Wang, Wei-chao, 63Wang, Wei-guo, 63Wathen, Andrew J., 15, 15, 27Watkins, David S., 59Weber, Marcus, 18Wei, Yimin, 33, 43Weisbecker, Clement, 60Weiss, Jan-Philipp, 31Weng, Peter Chang-Yi, 39Willbold, Carina, 41Wirth, Fabian, 15Wittum, Gabriel, 26Womersley, Robert S., 65Wu, Chin-Tien, 42Wu, Minghao, 51Wu, Xunxun, 12Wülling, Wolfgang, 40Wyatt, Sarah, 11

XXia, Jianlin, 58, 58, 60Xu, Qingxiang, 43Xu, Shufang, 63Xue, Fei, 37Xue, Jungong, 63

YYamamoto, Kazuma, 45Yamanaka, Naoya, 45Yamazaki, Ichitaro, 45Yavneh, Irad, 10Ye, Qiang, 39Ye, Xuancan, 27Yıldırim, E. Alper, 55Yildiztekin, Kemal, 33Yuan, Xiaoming, 56

ZZangré, Ibrahim, 19Zaslavsky, Mikhail, 17Zemach, Ran, 10Zenadi, Mohamed, 34Zhang, Hong, 46Zhang, Jiani, 50Zhang, Qiang, 50Zhang, Wenxing, 56Zhao, Tao, 25Zhlobich, Pavel, 37Ziȩtak, Krystyna, 8Zikatanov, Ludmil T., 11Zimmermann, Karel, 49Zinemanas, Alejandro, 32Zounon, Mawussi, 46

Zouros, Grigorios, 19Zuk, Or, 18Zulehner, Walter, 20, 20


MS 1. Recent advances in matrix functionsTalk 1. Computational issues related to the geometric meanof structured matricesIn several applications it is required to compute the geometricmean of a set of positive definite matrices. In certain cases, likein the design of radar systems, the matrices are structured, say,they are Toeplitz, and one expects that the mean still keeps thesame structure.Unfortunately, the available definitions of geometric mean, likethe Karcher mean, do not generally maintain the structure of theinput matrices.In this talk we introduce a definition of mean which preservesthe structure, analyze its properties and present algorithms for itscomputation.Dario A. BiniDipartimento di MatematicaUniversità di Pisa, [email protected]

Bruno IannazzoDipartimento di Matematica e InformaticaUniversità di Perugia, [email protected]

Talk 2. Efficient, communication-minimizing algorithms forthe symmetric eigenvalue decomposition and the singularvalue decompositionWe propose algorithms for computing the symmetric eigenvaluedecomposition and the singular value decomposition (SVD) thatminimize communication in the asymptotic sense whilesimultaneously having arithmetic operation costs within a factor3 of that for the most efficient existing algorithms. The essentialcost for the algorithms is in performing QR factorizations, ofwhich we require no more than six for the symmetriceigenproblem and twelve for the SVD. We establish backwardstability under mild assumptions, and numerical experimentsindicate that our algorithms tend to yield decompositions withconsiderably smaller backward error and eigen/singular vectorscloser to orthogonal than existing algorithms.Yuji NakatsukasaSchool of MathematicsThe University of [email protected]

Nicholas J. HighamSchool of MathematicsThe University of [email protected]

Talk 3. The Padé approximation and the matrix sign functionIn the talk we focus on the properties of the Padé approximantsof a certain hypergeometric function on which the Padé familiesof iterations for computing the matrix sign and sector functionsare based. We have determined location of poles of the Padéapproximants and we have proved that all coefficients of thepower series expansions of the reciprocals of the denominatorsof the Padé approximants and of the power series expansions ofthe Padé approximants are positive. These properties are crucialin the the proof of the conjecture – stated by Laszkiewicz andZiȩtak, and extending the result of Kenney and Laub – on aregion of convergence of these Padé families of iterations.The talk is based on the paper by O. Gomilko, F. Greco, K.Ziȩtak and the paper by O. Gomilko, D.B. Karp, M. Lin, K.Ziȩtak. In the talk we also consider a certain different kind ofrational approximation to the sign function.

Krystyna ZiȩtakInstitute of Mathematics and Computer ScienceWrocław University of [email protected]

Talk 4. A recursive blocked schur algorithm for computingthe matrix square rootThe Schur algorithm for computing a matrix square root reducesthe matrix to the Schur triangular form and then computes asquare root of the triangular matrix. In this talk I will describe arecursive blocking technique in which the computation of thesquare root of the triangular matrix can be made rich in matrixmultiplication. Numerical experiments making appropriate useof level 3 BLAS show significant speedups over the pointalgorithm, both in the square root phase and in the algorithm as awhole. The excellent numerical stability of the point algorithm isshown to be preserved by recursive blocking. Recursive blockingis also shown to be effective for multiplying triangular matrices.Edvin DeadmanUniversity of [email protected]

Nicholas J. HighamSchool of MathematicsUniversity of [email protected]

Rui RalhaCenter of MathematicsUniversity of Minho, Portugalr [email protected]

MS 2. Methods for Toeplitz matrices and theirapplicationTalk 1. Toeplitz operators with matrix-valued symbols andsome (unexpected) applicationsWe discuss the eigenvalue distribution in the Weyl sense ofgeneral matrix-sequences associated to a symbol. As a specificcase we consider Toeplitz sequences generated by matrix-valued(non Hermitian) bounded functions. We show that the canonicaldistribution can be proved under mild assumptions on thespectral range of the given symbol. Finally some applicationsare introduced and discussed.Stefano Serra CapizzanoDipartimento di Fisica e MatematicaUniversità dell’Insubria - sede di Como, [email protected]

Talk 2. Fast approximation to the Toeplitz matrix exponentialThe shift-invert Lanczos (or Arnoldi) method is employed togenerate an orthonormal basis from the Krylov subspacecorresponding to the real Toeplitz matrix and an initial vector.The vectors and recurrence coefficients produced by this methodare exploited to approximate the Toeplitz matrix exponential.Toeplitz matrix inversion formula and rapid Toeplitzmatrix-vector multiplications are utilized to lower thecomputational costs. For convergence analysis, a sufficientcondition is established to guarantee that the error bound isindependent of the norm of the matrix. Numerical results andapplications to the computational finance are given todemonstrate the efficiency of the method.Hai-Wei SunFaculty of Science and TechnologyUniversity of Macau, [email protected]


Talk 3. Matrix algebras sequences can be spectrallyequivalent with ill-conditioned Toeplitz onesThe construction of fast and efficient iterative procedure oreffective multigrid schemes, requires the study of the spectrumof the matrix sequences {An}n, where{An}n = {P−1n (f)Tn(f)}n. In this talk, we focus on the casewhere Tn(f) is a Toeplitz matrix generated by a nonnegativereal function f , and Pn(f) denotes matrices belonging to tau orcirculant algebras. Assuming that the symbol f has discreteroots of non integer order, we will show that under suitableassumptions the spectrum of the matrix sequence {An}n isbounded by constants far away from zero and infinity. Using thedeveloped theory, we propose effective preconditioners and wegive hints for optimal multigrid schemes.Paris VassalosDept. of InformaticsAthens University of Economics and [email protected]

Dimitrios NoutsosDept. of MathematicsUniversity of [email protected]

Talk 4. Aggregation-based multigrid methods for ToeplitzmatricesAggregation and smoothed aggregation based multigrid methodscan be analyzed in the context of the convergence theory forToeplitz and circulant matrices. As in the aggregation-basedmultigrid methods, for generating symbols with a single isolatedzero at the origin aggregates are formed. The interpolation canthen be improved by applying an additional operator. Thisimprovement can be interpreted as the smoothing step in theoriginal smoothed aggregation method. Depending on theoriginal generating symbol, several smoothing steps can benecessary. Numerical examples show the efficiency of theaggregation based approach in the case of Toeplitz and circulantmatrices.Matthias BoltenDepartment of Mathematics and ScienceUniversity of Wuppertal, [email protected]

Marco DonatelliDipartimento di Fisica e MatematicaUniversità dell’Insubria - sede di Como, [email protected]

Thomas HuckleDept. of InformaticsTechnische Universität München, [email protected]

MS 3. Matrix factorizations and applicationsTalk 1. Classes of matrices with bidiagonal factorizationMatrices with a bidiagonal decomposition satisfying some signrestrictions are analyzed. They include all nonsingular totallypositive matrices, their matrices opposite in sign and theirinverses, as well as tridiagonal nonsingular H-matrices.Properties of these matrices are presented and the bidiagonalfactorization can be used to perform computations with highrelative accuracy.Álvaro BarrerasDept. of Applied Mathematics / IUMAUniversidad de [email protected]

Juan Manuel PeñaDept. of Applied Mathematics / IUMAUniversidad de [email protected]

Talk 2. Cholesky factorization for singular matricesDirect and iterative solution methods for linear least-squaresproblems have been studied in Numerical Linear Algebra. Partof the difficulty for solving least-squares problems is the factthat many methods solve the system by implicitly solving thenormal equations ATAx = AT b with A ∈ Rn×m and b ∈ Rn.In this talk we consider this problem when A is a rank deficientmatrix. Then, ATA is a positive semidefinite matrix and itsCholesky factorization is not unique. So, we introduce a fullrank Cholesky decomposition LLT of the normal equationsmatrix without the need to form the normal matrix itself. Wepresent two algorithms to compute the entries of L by rows (orby columns) with the corresponding error analysis. Numericalexperiments illustrating the proposed algorithms are given.Rafael CantóDept. of Applied MathematicsUniversitat Politècnica de Valè[email protected]

Ana M. UrbanoDept. of Applied MathematicsUniversitat Politècnica de Valè[email protected]

Marı́a J. PeláezDept. of MathematicsUniversidad Católica del [email protected]

Talk 3. Applications of the singular value decomposition toperturbation theory of eigenvalues of matrix polynomialsIn this talk, motivated by a problem posed by Wilkinson, westudy the coefficient perturbations of a n× n matrix polynomialto n× n matrix polynomials which have a prescribed eigenvalueof specified algebraic multiplicity and index of annihilation. Foran n× n matrix polynomial P (λ) and a given scalar µ ∈ C, weintroduce two weighted spectral norm distances, Er(µ) andEr,k(µ), from P (λ) to the n× n matrix polynomials that have µas an eigenvalue of algebraic multiplicity at least r and to thosethat have µ as an eigenvalue of algebraic multiplicity at least rand maximum Jordan chain length exactly k, respectively. Thenwe obtain a singular value characterization of Er,1(µ), andderive a lower bound for Er,k(µ) and an upper bound for Er(µ),constructing associated perturbations of P (λ).Panayiotis PsarrakosDept. of MathematicsNational Technical University of [email protected]

Nikolaos PapathanasiouDept. of MathematicsNational Technical University of [email protected]

Talk 4. On reduced rank nonnegative matrix factorizationfor symmetric nonnegative matricesFor a nonnegative matrix V ∈ Rm,n, the nonnegative matrixfactorization (NNMF) problem consists of finding nonnegativematrix factors W ∈ Rm,r and H ∈ Rr,n such that V ≈WH .We consider the algorithm provided by Lee and Seung whichfinds nonnegative W and H such that ‖V −WH‖F isminimized. For the case m = n and in which V is symmetric,we present results concerning when the best approximate


factorization results in the product WH being symmetric and oncases in which the best approximation cannot be a symmetricmatrix. Results regarding other special cases as well asapplications are also discussed.Minerva CatralDept. of MathematicsXavier [email protected]

Lixing HanDept. of MathematicsUniversity of [email protected]

Michael NeumannDept. of MathematicsUniversity of Connecticut

Robert J. PlemmonsDept. of Mathematics and Computer ScienceWake Forest [email protected]

MS 4. Algorithms on manifolds of low-rank matricesand tensorsTalk 1. Low rank dynamics for computing extremal points ofreal and complex pseudospectraWe consider the real ε-pseudospectrum of a square matrix,which is the set of eigenvalues of all real matrices that areε-close to the given matrix, where closeness is measured ineither the 2-norm or the Frobenius norm.We characterize extremal points and compare the situation withthat for the unstructured ε-pseudospectrum. We presentdifferential equations for low rank (1 and 2) matrices for thecomputation of the extremal points of the pseudospectrum.Discretizations of the differential equations yield algorithms thatare fast and well suited for sparse large matrices. Based on theselow-rank differential equations, we further obtain an algorithmfor drawing boundary sections of the structured pseudospectrumwith respect to both considered norms.Nicola GuglielmiDipartimento di MatematicaUniversità di L’Aquila, [email protected]

Christian LubichMathematisches InstitutUniversität Tü[email protected]

Talk 2. Parametric model order reduction using stabilizedconsistent interpolation on matrix manifoldsA robust method for interpolating reduced-order linear operatorson their matrix manifolds is presented. Robustness is achievedby enforcing consistency between the different sets ofgeneralized coordinates underlying different instances ofparametric reduced-order models (ROMs), and explicitlystabilizing the final outcome of the interpolation process.Consistency is achieved by transforming the ROMs beforeinterpolation using a rotation operator obtained from the solutionof a generalized orthogonal Procrustes problem. Stabilization isachieved using a novel real-time algorithm based on semidefiniteprogramming. The overall method is illustrated with its on-lineapplication to the parametric fluid-structure analysis of awing-store configuration.David Amsallem

Department of Aeronautics and AstronauticsStanford [email protected]

Charbel FarhatDepartment of Aeronautics and AstronauticsDepartment of Mechanical EngineeringInstitute for Computational Methods in EngineeringStanford [email protected]

Talk 3. Treatment of high-dimensional problems by low-rankmanifolds of tensorsMany problems in e.g. natural sciences, data mining andstatistics are naturally posed as high-dimensionalproblems.Tensor product representations parametrize theseproblem on approximation manifolds, often fixed by a givenmaximal rank for the tensor approximation. A relatively newformat is the HT/TT format as developed by Hackbusch(Leipzig) and Oseledets/Tyrtyshnikov (Moscow), whichovercomes the shortcomings of older formats and gives a stableand often sparse opportunity to represent high-dimensionalquantities, so that the treatment of e.g. high-dimensional partialdifferential equations is on the verge of realization. In this talk, ageneral framework to realize such tasks in data-sparse tensorformats is presented. For the HT/TT format, we present sometheoretical as well as algorithmic results for the treatment ofhigh-dimensional optimization tasks and high-dimensionalevolution equations.Thorsten RohwedderInstitut für MathematikTechnische Universität [email protected]

Talk 4. Local convergence of alternating optimization ofmultivariate functions in the presence of scalingindeterminaciesAn easy and widely used approach to minimize functions withrespect to certain tensor formats (such as CP, Tucker, TT or HT)is the alternating optimization algorithm, also called nonlinearGauss–Seidel method. A prominent example is thePARAFAC-ALS algorithm. Due to the usual non-uniqueness oftensor representations, standard convergence results fornonlinear Gauss-Seidel are usually not directly applicable. Inthis talk we present a quite general approach to prove localconvergence, based on a geometric viewpoint, which regardstensors of fixed rank as orbits of a Lie group generatingequivalent representations.André UschmajewInstitut für MathematikTechnische Universität (TU) [email protected]

MS 5. Advances in algebraic multigrid - Newapproaches and applicationsTalk 1. Algebraic collocation coarse approximation multigridMost algebraic multigrid (AMG) methods define the coarseoperators by applying the (Petrov-)Galerkin coarseapproximation where the sparsity pattern and operatorcomplexity of the multigrid hierarchy is dictated by themultigrid prolongation and restriction. Therefore, AMGalgorithms usually must settle on some compromise between thequality of these operators and the aggressiveness of thecoarsening, which affects their rate of convergence and operatorcomplexity. In this paper we propose an algebraic generalization


of the collocation coarse approximation (CCA) approach ofWienands and Yavneh, where the choice of the sparsity patternof the coarse operators is independent of the choice of thehigh-quality transfer operators. The new algorithm is based onthe aggregation framework (smoothed and non-smoothed).Using a small set of low-energy eigenvectors, it computes thecoarse grid operator by a weighted least squares process.Numerical experiments for two dimensional diffusion problemswith sharply varying coefficients demonstrate the efficacy andpotential of this multigrid algorithm.Eran TreisterDepartment of Computer ScienceTechnion—Israel Institute of Technology, [email protected]

Ran ZemachDepartment of Computer ScienceTechnion—Israel Institute of Technology, [email protected]

Irad YavnehDepartment of Computer ScienceTechnion—Israel Institute of Technology, [email protected]

Talk 2. Energy-minimization interpolation for adaptivealgebraic multigridAdaptive algebraic multigrid (AMG) methods automaticallydetect the algebraically smooth error for a linear system and assuch, are robust black box approaches for solving difficultproblems. However, the two main families of methods,Bootstrap AMG (BAMG) and adaptive smoothed aggregation(αSA), suffer from drawbacks, such as noisy candidate vectors(BAMG) and potentially high operator complexity, especiallyfor scalar problems, (αSA). This work is intended to addresssome of these drawbacks by combining elements of BAMG andαSA through an energy-minimization interpolation framework.While the approach is general, the challenging, motivatingproblem is a biquadratic discretization of anisotropic diffusion.Jacob B. SchroderCenter for Applied Scientific ComputingLawrence Livermore National Laboratory (LLNL), [email protected]

Robert D. FalgoutCenter for Applied Scientific ComputingLawrence Livermore National Laboratory (LLNL), [email protected]

Talk 3. Algebraic multigrid (AMG) for complex networkcalculationsClustering, ranking, or measuring distance for vertices onscale-free graphs are all computational task of interest. Suchcalculations may be obtained by solving eigensystems or linearsystems involving matrices whose sparsity structure is related toan underlying scale-free graph. For many large systems ofinterest, classical iterative solvers (such as conjugate gradientand Lanczos) converge with prohibitively slow rates, due toill-conditioned matrices and small spectral gap ratios. Efficientlypreconditioning these systems with multilevel methods isdifficult due to the scale-free topology. For some large modelproblems and real-world networks, we investigate theperformance of a few AMG-related coarsening approaches.Geoffrey D. SandersCenter for Applied Scientific ComputingLawrence Livermore National Laboratory (LLNL), [email protected]

Van Emden HensonCenter for Applied Scientific ComputingLawrence Livermore National Laboratory (LLNL), [email protected]

Panayot S. VassilevskiCenter for Applied Scientific ComputingLawrence Livermore National Laboratory (LLNL), [email protected]

Talk 4. The polynomial of best uniform approximation to 1/xas smoother in two grid methodsWe discuss a simple convergence analysis of two level methodswhere the relaxation on the fine grid uses the polynomial of bestapproximation in the uniform norm to 1/x on a finite intervalwith positive endpoints. The construction of the latterpolynomial is of interest by itself, and we have included aderivation of a three-term recurrence relation for computing thispolynomial. We have also derived several inequalities related tothe error of best approximation, monotonicity of the polynomialsequence, and positivity which we applied in the analysis oftwo-level methods.Ludmil T. ZikatanovDepartment of MathematicsThe Pennsylvania State University, [email protected]

Johannes KrausJohann Radon Institute for Computational and Applied Mathematics(RICAM), [email protected]

Panayot S. VassilevskiCenter for Applied Scientific ComputingLawrence Livermore National Laboratory (LLNL), [email protected]

MS 6. Recent advances in fast iterative solvers - Part Iof IITalk 1. Challenges in analysis of Krylov subspace methodsThe current state-of-the art of iterative solvers is the outcome ofthe tremendous algorithmic development over the last fewdecades and of investigations of how to solve given problems. Inthis contribution we focus on Krylov subspace methods andmore on the dual question why things do or do not work. Inparticular, we will pose and discuss open questions such as whatthe spectral information tells us about the behaviour of Krylovsubspace methods, to which extent we can relax the accuracy oflocal operations in inexact Krylov subspace methods withoutcausing an unwanted delay, how important is considering ofrounding errors in various algorithmic techniques, whether it isuseful to view Krylov subspace methods as matching momentmodel reduction, and how the algebraic error can be includedinto locally efficient and fully computable a-posteriori errorbounds for adaptive PDE solvers.Zdeněk StrakošCharles University in Prague and Academy of Science of the [email protected]

Jörg LiesenInstitute of MathematicsTechnical University of [email protected]

Talk 2. Updating preconditioners for parameterized systemsParameterized linear systems arise in a range of applications,such as model reduction, acoustics, and inverse problems basedon parametric level sets. Computing new preconditioners for


many small changes in parameter(s) would be very expensive.However, using one or only a few preconditioners for all systemsleads to an excessive total number of iterations. We showstrategies to efficiently compute effective multiplicative updatesto preconditioners. This has the advantage that, for a slightincrease in overhead, the update is more or less independent ofthe original preconditioner used.Eric de SturlerDepartment of MathematicsVirginia [email protected]

Sarah WyattDepartment of MathematicsVirginia [email protected]

Serkan GugercinDepartment of MathematicsVirginia [email protected]

Talk 3. Efficient preconditioning techniques for two-phaseflow simulationsIn this talk we present efficient preconditioning strategies,suitable for the iterative solution of algebraic systems, arising innumerical simulations of two-phase flow problems, modelled bythe Cahn-Hilliard equation.In this work, we decompose the original Cahn-Hilliard equation,which is nonlinear and of fourth-order, into a system of twosecond-order equations for the so-called ’concentration’ and’chemical potential’. The so-obtained nonlinear system isdiscretized using the finite element method and solved by twovariants of the inexact Newton method. The major focus of thework is to construct a preconditioner for the correcpondingJacobian, which is of block two-by-two form. The proposedpreconditioning techniques are based on approximatefactorization of the discrete Jacobian and utilise to a full extentthe properties of the underlying matrices.We propose a preconditioning method that reduces the problemof solving the non-symmetric discrete Cahn-Hilliard system tothe problem of solving systems with symmetric positive definitematrices, where off-the-shelf multilevel and multigrid algorithmsare directly applicable. The resulting iterative method exhibitsoptimal convergence and computational complexity properties.The efficiency of the resulting preconditioning method isillustrated via various numerical experiments, including largescale examples of both 2D and 3D problems.The preconditioning techniques are more generally applicablefor any algebraic system of the same structure as, e.g., whensolving complex symmetric linear systems.M. NeytchevaInstitute for Information TechnologyUppsala [email protected]

Owe AxelssonInstitute of GeonicsAcademy of Sciences of the Czech Republic, [email protected]

Petia BoyanovaInstitute for Information TechnologyUppsala [email protected]

Martin KronbichlerInstitute for Information TechnologyUppsala University

[email protected]

Xunxun WuInstitute for Information TechnologyUppsala [email protected]

Talk 4. Preconditioners in liquid crystal modellingLiquid crystal displays are ubiquitous in modern life, being usedextensively in monitors, televisions, gaming devices, watches,telephones etc. Appropriate models feature characteristic lengthand time scales varying by many orders of magnitude, whichprovides difficult numerical challenges to those trying tosimulate real-life dynamic industrial situations. The efficientsolution of the resulting linear algebra sub-problems is of crucialimportance for the overall effectiveness of the algorithms used.In this talk we will present some examples of saddle-pointsystems which arise in liquid crystal modelling and discuss theirefficient solution using appropriate preconditioned iterativemethods.Alison RamageDept of Mathematics and StatisticsUniversity of StrathclydeGlasgow, [email protected]

Chris NewtonNext Generation Displays GroupHewlett-Packard LaboratoriesBristol, [email protected]

MS 7. Application of statistics to numerical linearalgebra algorithms - Part I of IITalk 1. Fast linear system solvers based on randomizationtechniquesWe illustrate how dense linear algebra calculations can beenhanced by randomizing general or symmetric indefinitesystems. This approach, based on a multiplicativepreconditioning of the initial matrix, revisits the work from[Parker, 1995]. It enables us to avoid pivoting and then to reducesignificantly the amount of communication. This can beperformed at a very affordable computational price whileproviding a satisfying accuracy. We describe solvers based onrandomization that take advantage of the latest generation ofmulticore or hybrid multicore/GPU machines and we comparetheir Gflop/s performance with solvers from standard parallellibraries.Marc BaboulinInria Saclay Île-de-FranceUniversity Paris-Sud, [email protected]

Dulceneia BeckerUniversity of Tennessee, [email protected]

Jack DongarraUniversity of Tennessee, [email protected]

Stanimire TomovUniversity of Tennessee, [email protected]

Talk 2. Numerical issues in randomized algorithmsRandomized algorithms are starting to find their way into a widevariety of applications that give rise to massive data sets. Thesealgorithms downsize the enormous matrices by picking and


choosing only particular columns or rows, thereby producingpotentially huge savings in storage and computing speed.Although randomized algorithms can be fast and efficient, notmuch is known about their numerical properties. We will discussthe numerical sensitivity and stability of randomized algorithms,as well as the error due to randomization, and the effect of thecoherence of the matrix. Algorithms under consideration includematrix multiplication, least squares solvers, and low-rankapproximations.Ilse IpsenDepartment of MathematicsNorth Carolina State University, [email protected]

Talk 3. Near-optimal column based matrix reconstructionWe consider low-rank reconstruction of a matrix using a subsetof its columns and we present asymptotically optimal algorithmsfor both spectral norm and Frobenius norm reconstruction. Themain tools we introduce to obtain our results are: (i) the use offast approximate SVD-like decompositions for column-basedmatrix reconstruction, and (ii) two deterministic algorithms forselecting rows from matrices with orthonormal columns,building upon the sparse representation theorem fordecompositions of the identity that appeared in [Batson,Spielman, Srivastava, 2011].Christos BoutsidisMathematical Sciences DepartmentIBM T. J. Watson Research Center, [email protected]

Petros DrineasComputer Science DepartmentRensselaer Polytechnic Institute, [email protected]

Malik Magdon-IsmailComputer Science DepartmentRensselaer Polytechnic Institute, [email protected]

Talk 4. Numerical experiments with statistical conditionestimationIn this talk we present the results of some numerical experimentsillustrating the use of statistical condition estimation (SCE).After a brief review of SCE, the use of the technique isdemonstrated on a few topics of general interest including theestimation of the condition of large sparse linear systems.Alan J. LaubDepartment of MathematicsUniversity of California Los Angeles, [email protected]

MS 8. Rational Krylov methods: analysis andapplications - Part I of IITalk 1. Solving Sylvester equations through rational GalerkinprojectionsRecently (B. Beckermann, An error analysis for rationalGalerkin projection applied to the Sylvester equation, SIAM J.Num. Anal. 49 (2012), 2430-2450), we suggested a new erroranalysis for the residual of Galerkin projection onto rationalKrylov spaces applied to a Sylvester equation with a rank 1right-hand side. In this talk we will consider more generallysmall rank right-hand sides, where block Krylov methods andtangential interpolation problems play an important role.Bernhard BeckermannDept. of Mathematics

University of [email protected]

Talk 2. Stability-corrected spectral Lanczos decompositionalgorithm for wave propagation in unbounded domainsApplying Krylov subspace methods to exterior wave fieldproblems has become an active topic of recent research. In thispaper, we introduce a new Lanczos-based solution method viastability-corrected operator exponents, allowing us to constructstructure-preserving reduced-order models (ROMs) respectingthe delicate spectral properties of the original scatteringproblem. The ROMs are unconditionally stable and are based ona renormalized Lanczos algorithm, which enables us toefficiently compute the solution in the frequency and timedomain. We illustrate the performance of our method through anumber of numerical examples in which we simulate 2Delectromagnetic wave propagation in unbounded domains.Rob RemisFaculty of Electrical Engineering, Mathematics and Computer ScienceDelft University of [email protected]

Vladimir DruskinSchlumberger-Doll [email protected]

Talk 3. Generalized rational Krylov decompositionsThe notion of an orthogonal rational Arnoldi decomposition, asintroduced by Axel Ruhe, is a natural generalization of thewell-known (polynomial) Arnoldi decomposition. Generalizedrational Krylov decompositions are obtained by removing theorthogonality assumption. Such decompositions are interestinglinear algebra objects by themselves and we will study some oftheir algebraic properties, as well as the rational Krylov methodsthat can be associated with them.Stefan GüttelMathematical InstituteUniversity of [email protected]

Talk 4. Interpolatory model reduction strategies for nonlinearparametric inversionWe will show how reduced order models can significantlyreduce the cost of general inverse problems approached throughparametric level set methods. Our method drastically reduces thesolution of forward problems in diffuse optimal tomography(DOT) by using interpolatory, i.e. rational Krylov based,parametric model reduction. In the DOT setting, these surrogatemodels can approximate both the cost functional and associatedJacobian with little loss of accuracy and significantly reducedcost.Serkan GugercinDept. of MathematicsVirginia [email protected]

Christopher A. BeattieDept. of MathematicsVirginia [email protected]

Saifon ChaturantabutDept. of MathematicsVirginia [email protected]

Eric de SturlerDept. of MathematicsVirginia [email protected]


Misha E. KilmerDept. of MathematicsTufts [email protected]

MS 9. New trends in tridiagonal matrices - Part I of IITalk 1. Direct and inverse problems on pseudo-JacobimatricesA theorem of Friedland and Melkman states the unique recoveryof a non-negative Jacobi matrix from the spectra of its upper andlower principal submatrices obtained by deleting the kth row andcolumn. Here this result is revisited and generalized. Otherrelated problems are also investigated, including existence anduniqueness theorems.Natália BebianoDepartment of MathematicsUniversity of Coimbra3001-454 [email protected]

Susana FurtadoFaculty of EconomicsUniversity of Porto4200-464 [email protected]

J. da ProvidênciaDepartment of PhysicsUniversity of Coimbra3004-516 [email protected]

Talk 2. Schwartz’s matrices and generalized HurwitzpolynomialsWe present solutions of direct and inverse spectral problems fora kind of Schwarz’s matrices (tridiagonal matrices with only onenonzero main-diagonal entry). We study dependence of spectraof such matrices on the signs of their off-main-diagonal entries.We show that for certain distributions of those signs, thecharacteristic polynomial of the correspondent Schwarz’s matrixis a generalized Hurwitz polynomial. Recall that a realpolynomial p(z) = p0(z2) + zp1(z2), where p0 and p1 are theeven and odd parts of p, respectively, is generalized Hurwitz ifand only if the zeroes of p0 and p1 are real, simple andinterlacing.Mikhail TyaglovInstitut für MathematikTechnische Universität BerlinSekretariat MA 4-5Straße des 17. Juni 13610623 [email protected]

Talk 3. On the Moore-Penrose inverse of singular, symmetricand periodic Jacobi M-matricesWe aim here at determining the Moore–Penrose inverse, J† ofany singular, symmetric and periodic Jacobi M–matrix J, boththroughout direct computations or considering it as aperturbation of a singular, symmetric and nonperiodic JacobiM–matrix. We tackle the problem by applying methods fromthe operator theory on finite networks, since the off–diagonalentries of J can be identified with the conductance function of aweighted n–cycle. Then, J appears as a positive–semidefinite

Schrödinger operator on the cycle and hence, J† is nothing elsethat the corresponding Green operator.We also consider the problem of characterizing when J† is itselfan M -matrix.Andrés M. EncinasDepartament de Matemàtica Aplicada IIIUniversitat Politècnica de Catalunya08034 [email protected]

Enrique BenditoDepartament de Matemàtica Aplicada IIIUniversitat Politècnica de Catalunya08034 [email protected]

Ángeles CarmonaDepartament de Matemàtica Aplicada IIIUniversitat Politècnica de Catalunya08034 [email protected]

Margarida MitjanaDepartament de Matemàtica Aplicada IUniversitat Politècnica de Catalunya08034 [email protected]

Talk 4. The commutant of the tridiagonal patternWe consider patterns that allow real commutativity with anirreducible tridiagonal n-by-n pattern. All are combinatoriallysymmetric. All also allow a complex symmetric commuting pair,but only some allow a real symmetric commuting pair. We alsoshow that any matrix that commutes with an irreducibletridiagonal matrix satisfies certain ratio equations.Generalizations to matrices with tree patterns are alsoconsidered.Charles R. JohnsonDepartment of MathematicsCollege of William and MaryPO Box 8795Williamsburg, VA [email protected]

MS 10. Numerical algorithms for switching systems:from theory to applicationsTalk 1. Observer design for hybrid systemsThe state estimation problem has been the subject of intensivestudy for many years by both the computer science communityin the discrete domain and the control community in thecontinuous domain, but only scantly investigated in the hybridsystem domain.In this talk, we present a design methodology for dynamicalobservers of hybrid systems with linear continuous-timedynamics, which reconstruct the complete state from theknowledge of the inputs and outputs of a hybrid plant.We demonstrate the methodology by building a hybrid observerfor an industrial automotive control problem: on-lineidentification of the actual engaged gear.Maria Domenica Di BenedettoUniversity of L’[email protected]


Talk 2. About polynomial instability for linear switchedsystemsIn this talk we present recent results on the characterization ofmarginal instability for linear switched systems. Our maincontribution consists in pointing out a resonance phenomenonassociated with marginal instability. In particular we derive anupper bound of the norm of the state at time t, which ispolynomial in t and whose degree is computed from theresonance structure of the system. We also derive analogousresults for discrete-time linear switched systems.Paolo MasonLaboratoire des Signaux et Systè[email protected]

Yacine ChitourLaboratoire des Signaux et SystèmesUniversité Paris [email protected]

Mario SigalottiCMAP, INRIA [email protected]

Talk 3. Stability and stabilization of positive switchedsystems: state of the art and open problemsA positive switched system (PSS) consists of a family of positivestate-space models and a switching law, specifying when andhow the switching among the various models takes place. Thisclass of systems has some interesting practical applications:PSS’s have been adopted for describing networks employingTCP and other congestion control applications, for modelingconsensus and synchronization problems, and, quite recently, fordescribing the viral mutation dynamics under drug treatment.In the talk we will provide a comprehensive picture of theconditions for stability and for stabilizability, and we will pointout some open problems.Maria Elena ValcherDept. of Information EngineeringUniversity of [email protected]

Ettore FornasiniDept. of Information EngineeringUniversity of [email protected]

Talk 4. The joint spectral radius for semigroups generated byswitched differential algebraic equationsWe introduce the joint spectral radius for matrix semigroups thatare generated by switched linear ordinary differential equationswith jumps. The jumps are modeled by projectors which areassumed to commute with the generators of the flow. This setupcovers switched differential algebraic equations. It is shown thatan exponential growth rate can only be defined if the discretesemigroup generated by the projections is product bounded.Assuming this is true we show that Barabanov norms may bedefined in the irreducible case and that a converse Lyapunovtheorem holds. Some further properties of the exponentialgrowth rate are discussed.Fabian WirthDept. of MathematicsUniversity of Würzburg, [email protected]

Stephan TrennDept. of MathematicsTechnical University of Kaiserslautern, [email protected]

MS 11. Recent advances in fast iterative solvers -Part II of IITalk 1. Combination preconditioning of saddle-point systemsfor positive definitenessThere are by now many preconditioning techniques forsaddle-point systems but also a growing number of applicationswhere such are required. In this talks we will discusspreconditioners which preserve self-adjointness in non-standardinner products and the combination of such preconditioners asintroduced by Martin Stoll and the first author in 2008.Here we will show how two preconditioners which ensureself-adjointness in different inner products, but which are bothindefinite may be combined to yield a positive definiteself-adjoint preconditioned system in a third inner product whichthus allows robust application of the Hestenes Steifel ConjugateGradient method in that inner product.Andrew J. WathenMathematical InstituteOxford University, [email protected]

Jennifer PestanaMathematical InstituteOxford University, [email protected]

Talk 2. Preconditioned iterative methods for nonsymmetricmatrices and nonstandard inner productsThe convergence of a minimum residual method applied to alinear system with a nonnormal coefficient matrix is not wellunderstood in general. This can make choosing an effectivepreconditioner difficult. In this talk we present a new GMRESconvergence bound. We also show that the convergence of anonstandard minimum residual method, applied to apreconditioned system, is bounded by a term that dependsprimarily on the eigenvalues of the preconditioned coefficientmatrix, provided the preconditioner and coefficient matrix areself-adjoint with respect to nearby Hermitian sesquilinear forms.We relate this result to the convergence of standard methods.Jennifer PestanaMathematical InstituteUniversity of [email protected]

Andrew J. WathenMathematical InstituteUniversity of [email protected]

Talk 3. Multi-preconditioned GMRESStandard Krylov subspace methods only allow the user to choosea single preconditioner. In many situations, however, there is no‘best’ choice, but a number of possible candidates. In this talkwe describe an extension of GMRES, multi-preconditionedGMRES, which allows the use of more than one preconditioner,and combines their properties in an optimal way. As well asdescribing some theoretical properties of the new algorithm wewill present numerical results which highlight the utility of theapproach.Tyrone ReesNumerical Analysis GroupRutherford Appleton [email protected]

Chen GreifDept. of Computer ScienceUniversity of British Columbia


[email protected]

Daniel B. SzyldDept. of MathematicsTemple [email protected]

Talk 4. Bounds on the eigenvalues of indefinite matricesarising from interior-point methodsInterior-point methods feature prominently in the solution ofconstrained optimization problems, and involve the need to solvea sequence of 3× 3 block indefinite matrices that becomeincreasingly ill-conditioned throughout the iteration. Mostsolution approaches are based on reducing the system size usinga block Gaussian elimination procedure. In this talk we useenergy estimates to obtain bounds on the eigenvalues of theoriginal, augmented matrix, which indicate that the spectralstructure of this matrix may be favorable compared to matricesobtained by performing a partial elimination of variables beforesolving the system.Chen GreifDepartment of Computer ScienceThe University of British [email protected]

Erin MouldingDepartment of MathematicsThe University of British [email protected]

Dominique OrbanMathematics and Industrial Engineering DepartmentEcole Polytechnique de [email protected]

MS 12. Application of statistics to numerical linearalgebra algorithms - Part II of IITalk 1. Spectral graph theory, sampling matrix sums, andnear-optimal SDD solversWe present a near-optimal solver for Symmetric DiagonallyDominant (SDD) linear systems. The solver is a great exampleof the power of statistical methods in linear algebra and inparticular of sampling sums of positive semi-definite matrices.Crucial to the speed of the solver is the ability to perform fastsampling. In turn, key to fast sampling are low-stretch spanningtrees, a central notion in spectral graph theory and combinatorialpreconditioning. We will see that a low-stretch tree is essentiallya ‘spectral spine’ of a graph Laplacian, allowing us to create ahierarchy of spectrally similar graphs which lends itself to thevery fast multilevel solver.Ioannis KoutisComputer Science DepartmentUniversity of Puerto [email protected]

Gary MillerComputer Science DepartmentCarnegie Mellon University, [email protected]

Richard PengComputer Science DepartmentCarnegie Mellon University, [email protected]

Talk 2. Implementation of a randomization algorithm fordense linear algebra librariesRandomization algorithms are an alternative to pivoting forfactoring dense matrices to solve systems of linear equations.These techniques are more suitable to parallel architectures

when compared to pivoting, requiring a reduced amount ofcommunication and no synchronization during the factorization.The core kernel requires the multiplication of sparse matriceswith a specific structure. The main issue in implementing suchalgorithms resides in the data dependency patterns, especiallyfor the symmetric case. An implementation for the PLASMAlibrary is described and traces are presented, together withperformance data.Dulceneia BeckerUniversity of Tennessee, [email protected]

Marc BaboulinInria Saclay Île-de-FranceUniversity Paris-Sud, [email protected]

Jack DongarraUniversity of Tennessee, [email protected]

Talk 3. Implementing randomized matrix algorithms inlarge-scale parallel environmentsRecent work from theoretical computer science on developingrandomized matrix algorithms has recently led to thedevelopment of high-quality numerical implementations. Here,we describe our parallel iterative least-squares solver LSRN. Theparallelizable normal random projection in the preconditioningphase leads to a very well-conditioned system. Hence, thenumber of iterations is fully predictable if we apply LSQR or theChebyshev semi-iterative method to the preconditioned system.The latter method is particularly efficient for solving large-scaleproblems on clusters with high communication cost, e.g., onAmazon Elastic Compute Cloud clusters, that are increasinglycommon in large-scale data applications.Michael W. MahoneyDepartment of MathematicsStanford University, [email protected]

Talk 4. Random sampling preconditionersIn the talk we study the use of preconditioners based on randomsampling of rows for accelerating the solution of linear systems.We argue that the fusion of randomization with preconditioningis what enables fast and reliable algorithms.We will discuss both dense and sparse matrices. For densematrices, we will describe Blendenpik, a least-square solver fordense highly overdetermined systems that outperforms LAPACKby large factors, and scales significantly better than anyQR-based solver. For sparse matrices, we relate randomsampling preconditioners to fast SDD solvers, and generalizesome of the techniques to finite element matrices.Haim AvronMathematical Sciences DepartmentIBM T. J. Watson Research Center; [email protected]

Sivan ToledoDepartment of Computer ScienceTel-Aviv University, [email protected]

MS 13. Rational Krylov methods: analysis andapplications - Part II of IITalk 1. Rational Krylov methods for nonlinear matrixproblems


This talk is about the solution of non-linear eigenvalue problemsand linear systems with a nonlinear parameter. Krylov andRational Krylov methods are known to be efficient and reliablefor the solution of such matrix problems with a linear parameter.The nonlinear function can be approximated by a polynomial. Inearlier work, we suggested the use of Taylor expansions of thenonlinear function with an a priori undetermined degree. Thisled to the Taylor Arnoldi method that is an Arnoldi methodapplied to an infinite dimensional Companion linearization.When an interpolating polynomial is used instead of Taylorseries, there is a similar connection with the rational Krylovsubspace method applied on a linearization. The Krylovsubspaces enjoy similar properties as the linear case such asmoment matching and the convergence looks similar toconvergence for a linear problem. We present several choices ofpolynomials and also discuss ideas for future work.Karl MeerbergenDepartment of Computer [email protected]

Roel Van BeeumenDepartment of Computer [email protected]

Wim MichielsDepartment of Computer [email protected]

Talk 2. Block Gauss and anti-Gauss quadrature rules withapplication to networksThe symmetric and nonsymmetric block Lanczos processes canbe applied to compute Gauss quadrature rules for functionalswith matrix-valued measures. We show that estimates of upperand lower bounds for these functionals can be computedinexpensively by evaluating pairs of block Gauss and anti-Gaussrules. An application to network analysis is described.Lothar ReichelDept. of MathematicsKent State [email protected]

David MartinDept. of MathematicsKent State [email protected]

Talk 3. On optimality of rational Krylov based low-rankapproximations of large-scale matrix equationsIn this talk, we will discuss projection-based approximations forthe solution of Lyapunov equations of the form

AXET + EXAT +BBT = 0,

with A = AT , E = ET ∈ Rn×n and B ∈ Rn×m. Recently, arelation between minimizing the objective function

f :M→ R, X 7→ tr(XAXE +BBT

)on the manifoldM of symmetric positive semi-definite matricesof rank k and the L−norm defined by the operator

L := −E ⊗A−A⊗ E

together with the inner product 〈u, v〉L = 〈u,Lv〉 has beenshown. While so far this minimization problem was solved by

means of a Riemannian optimization approach, here we willdiscuss an interpolation-based method which leads to the sameresults but relies on projecting the original Lyapunov equationonto a rational Krylov subspace. It will turn out that this can beachieved by the iterative rational Krylov algorithm (IRKA).Besides a generalization for the case of A 6= AT , we will alsodiscuss an extension for more general equations of the form

AXE + FXB + CD = 0,

with A,F ∈ Rn×n, B,E ∈ Rm×m, C ∈ Rn×p andD ∈ Rp×m.Tobias BreitenComputational Methods in Systems and Control TheoryMax Planck Institute for Dynamics of Complex Technical [email protected]

Peter BennerComputational Methods in Systems and Control TheoryMax Planck Institute for Dynamics of Complex Technical [email protected]

Talk 4. Inverse problems for large-scale dynamical systems inthe H2-optimal model reduction frameworkIn this work we investigate the Rational Krylov subspace (RKS)projection method with application to the inverse problems. Wederive a representation for the reduced Jacobian as the productof a time-dependent and a stationary part. Then we show that theRKS satisfying the Meier-Luenberger necessary H2 optimalitycondition not only minimizes the approximation error butcompletely annuls its influence on the inversion result (even ifthe subspace is not optimal globally). More precisely, theapproximation error belongs to the (left) null-space of thereduced Jacobian. We compare inversion on such subspacesusing other nearly optimal RKS’s based on Zolotarev problemand adaptive pole selection algorithm.Mikhail ZaslavskySchlumberger-Doll [email protected]

Vladimir DruskinSchlumberger-Doll [email protected]

Valeria SimonciniDepartment of MathematicsUniversity of Bologna, [email protected]

MS 14. New trends in tridiagonal matrices - Part IIof IITalk 1. On generalized Jacobi matrices which are symmetricin Krein spacesI will give some motivations to introduce generalized Jacobimatrices of a special type. Then, some direct and inverseproblems for these matrices will be presented.Maxim DerevyaginInstitut für MathematikTechnische Universität BerlinSekretariat MA 4-5Straße des 17. Juni 13610623 [email protected]

Talk 2. On the characteristic function for Jacobi matricesFor a certain class of infinite Jacobi matrices with a discretespectrum it is introduced a characteristic function as an analytic


function on a suitable complex domain. It is shown that the zeroset of the characteristic function actually coincides with thepoint spectrum. As an illustration several explicitly solvableexamples are discussed.Pavel Štovı́čekDepartment of MathematicsFaculty of Nuclear Sciences and Physical EngineeringCzech Technical UniversityTrojanova 13120 00 PragueCzech [email protected]

Talk 3. Tridiagonal matrices in comb filtersIn the present talk we use some known and new results ontridiagonal matrices to compute the minimum mean square errorfor a decision feedback equalizer when the filter is a comb filter.We also apply those mathematical results on tridiagonal matricesto a problem in linear estimation with comb filters.Jesús Gutiérrez-GutiérrezCEIT and TecnunUniversidad de NavarraPaseo de Manuel Lardizabal, no. 1320018 Donostia - San Sebastiá[email protected]

Talk 4. The nullity theorem: forecasting structures in theinverses of sparse matricesThe Nullity Theorem for matrices was formulated by Markhamand Fiedler in 1986. At first sight, this theorem and its five-lineproof appear trivial. Examples show, however, that it is powerfultool in computations with sparse and structured rank matrices. Itis, e.g., a straightforward consequence of this theorem that theinverse of a tridiagonal is semiseparable, the inverse of a bandmatrix is higher order semiseparable, without even posingconstraints of irreducibility.We will reconsider the nullity theorem and extend it topredicting structures in LU and QR-factorizations.Raf VandebrilK.U. LeuvenDepartement Computerwetenschappen (Postbus 02402)Celestijnenlaan 200A3001 [email protected]

MS 15. Application of compressed sensing inBio-MedicineTalk 1. Evaluation of compressed sensing impact in cardiacsignals processing and transmissionSensor networks are a field which benefits significantly fromcompressed sensing (CS), as, for instance, quality of service, orbattery lifetime are directly improved by the subsequentreduction of traffic. Networks transmitting biomedical data, andwithin those, cardiac data, have particular advantages. ECG andPPG are the most studied 1D signals in the biomedical field, andwhere CS implementation has been more studied. One studyscenario is using the sparsity of wavelet decomposition of thesesignals, and Iterative Shrinkage/Thresholding algorithms. Focusis given in accuracy and computation overhead, the most criticalconstraints of cardiac data processing. Networking implicationsare quantified, for different types of real network models, as wellas the impact in signals quality, and on the extracted information

(heart rate, oxygen saturation, pulse wave velocity).Eduardo PinheiroInstituto de TelecomunicaesInstituto Superior Tcnico, Lisboa, [email protected]

Talk 2. Compressive sensing in drug discoveryThe design of new drugs is often based on certain interactionsbetween a small molecule (the drug) and a protein. Often a highaffinity between the small molecule and the protein is desirable.The affinity can be estimated by using statisticalthermodynamics. In order to provide statistical data,high-performance computing machines are used to explore theconformational space of the molecular system. Thecorresponding algorithms are based on simplified physicalmodels (force fields) for the interaction between the drugmolecule and the protein. These models mostly do not takequantum effects into account. The talk will present new ideas tobetter include quantum chemical information, it will providesome important application areas of molecular simulation indrug discovery, and it gives some hints about using compressivesensing in this field.Marcus WeberZuse Institute Berlin (ZIB), [email protected]

Talk 3. Reconstruction of bacterial communities using sparserepresentationDetermining the identities and frequencies of species present ina sample is a central problem in metagenomics, with scientific,environmental and clinical implications. A popular approach tothe problem is sequencing the Ribosomal 16s RNA gene in thesample using universal primers, and using variation in the gene’ssequence between different species to identify the speciespresent in the sample. We present a novel framework forcommunity reconstruction, based on sparse representation; whilemillions of microorganisms are present on earth, with known 16ssequences stored in a database, only a small minority (typically afew hundreds) are likely to be present in any given sample. Wediscuss the statistical framework, algorithms used and results interms of accuracy and species resolution.Or ZukBroad Institute, Cambridge, [email protected]

Talk 4. Sensing genome via factorizationSince the last decade the matrix factorization and dimensionreduction methods have been used for mining in genomics andproteomics. Also most recently the norm one optimization isemerging as a useful approach for this purpose. We propose ahybrid algorithm which uses the utility of SVD along withefficiency and robustness of norm one minimization forovercoming the shortcomings of each of these mentionedapproaches.Amir NiknejadCollege of Mount Saint Vincent, New York, [email protected]

MS 16. Preconditioning of non-normal linear systemsarising in scattering problemsTalk 1. Approximate deflation preconditioning methods forpenetrable scattering problemsIn this talk I consider the Lippmann-Schwinger (LS) integralequation for inhomogeneous acoustic scattering. I demonstrate


that spectral properties of the LS equations suggest that deflationbased preconditioning might be effective in accelerating theconvergence of a restarted GMRES method. Much of theconvergence results on deflation based preconditioning are basedon using exact invariant subspaces. I will present an analyticalframework for convergence theory of general approximatedeflation that is widely applicable. Furthermore, numericalillustrations of the spectral properties also reveal that asignificant portion of the spectrum is approximated well oncoarse grids. To exploit this, I develop a novel restarted GMRESmethod with adaptive preconditioning based on spectralapproximations on multiple grids.Josef SifuentesCourant Institute of Mathematical SciencesNew York [email protected]

Mark EmbreeDepartment of Computational and Applied MathematicsRice [email protected]

Talk 2. Direct approximate factoring of the inverseTo precondition a large and sparse linear system, two directmethods for approximate factoring of the inverse are devised.The algorithms are fully parallelizable and appear to be morerobust than the iterative methods suggested for the task. Amethod to compute one of the matrix subspaces optimally isderived. These approaches generalize the approximate inversepreconditioning techniques in several natural ways.Marko HuhtanenDepartment of Electrical and Information EngineeringUniversity of [email protected]

Mikko [email protected]

Talk 3. Regularization of singular integral operators as apreconditioning strategyIn this talk we consider the singular integral equation arising inelectromagnetic scattering on inhomogeneous objects in freespace. To understand the apparent poor convergence of iterativemethods, such as GMRES, we analyze the spectrum of both theintegral operator and the system matrix. It turns out that theconvergence is slowed down by dense spectral clusters, whoseorigin and location may be traced to the nontrivial essentialspectrum of the integral operator. We propose a multiplicativeregularizer which reduces the extent of these clusters and inconjunction with the deflation of largest-magnitude eigenvaluesmakes for a good preconditioner.Neil BudkoNumerical Analysis, Delft Institute of Applied MathematicsDelft University of [email protected]

Grigorios ZourosSchool of Electrical and Computer EngineeringNational Technical University of [email protected]

Talk 4. High-order shifted Laplace preconditioners for waveequationsShifted Laplace preconditioners techniques have beenintroduced by Erlangga, Vuik and Oosterlee (Applied NumericalMathematics, 2004) for solving PDEs problems related towave-like equations. The aim of this talk is to propose a

generalization of shifted Laplace preconditioning methods byusing operator representation combined with complex Padéapproximants. We will show that the resulting high-order shiftedLaplace preconditioners are highly efficient and robust for two-and three-dimensional scattering problems that exhibit complexgeometrical features (e.g. resonant structures). Furthermore, theconvergence is proved to be weakly frequency dependent.Xavier AntoineInstitut Elie Cartan de NancyUniversity of [email protected]

Christophe GeuzaineInstitut MontefioreUniversity of Liè[email protected]

Ibrahim ZangréInstitut Elie Cartan de NancyUniversity of [email protected]

MS 17. Markov ChainsTalk 1. Markov Chain properties in terms of column sums ofthe transition matrixQuestions are posed regarding the influence that the columnsums of the transition probabilities of a stochastic matrix (withrow sums all one) have on the stationary distribution, the meanfirst passage times and the Kemeny constant of the associatedirreducible discrete time Markov chain. Some new relationships,including some inequalities, and partial answers to the questions,are given using a special generalized matrix inverse that has notpreviously been considered in the literature on Markov chains.Jeffrey J. HunterSchool of Computing and Mathematical SciencesAuckland University of Technology, Auckland, New [email protected]

Talk 2. Hamiltonian cycle problem and Markov chainsWe consider the famous Hamiltonian cycle problem (HCP)embedded in a Markov decision process (MDP). Morespecifically, we consider the HCP as an optimization problemover the space of either stationary policies, or of occupationalmeasures induced by these stationary policies. This approachhas led to a number of alternative formulations and algorithmicapproaches involving researchers from a number of countries.These formulations exploit properties of a range of matrices thatusually accompany investigations of Markov chains. It will beshown that when these matrices are induced by the given graphsome of the graph’s underlying structures can be detected intheir matrix analytic properties.Jerzy FilarSchool of Computer Science, Engineering and MathematicsFlinders University, Bedford Park, SA, [email protected]

Talk 3. Inequalities for functions of transition matricesConsider an irreducible finite-state Markov chain on N states. Itis known that the N by N matrix vanishing on the diagonal andwhich is equal to the mean first passage matrix elsewhere, isinvertible. We prove that if N is greater than two, the diagonalentries of the inverse are negative, and obtain some relatedinequalities. Analogous results for a closely related matrix arederived as well. Joint with Michael Neumann and OlgaPryporova.


Iddo Ben-AriDepartment of MathematicsUniversity of Connecticut, Storrs, CT, United States of [email protected]

Talk 4. Compartmental systems and computation of theirstationary probability vectorsTo compute stationary probability vectors of Markov chainswhose transition matrices are cyclic of index p may be a difficulttask if p becomes large. A class of iterativeaggregation/disaggregation methods (IAD) is proposed toovercome the difficulty. It is shown that the rate of convergenceof the proposed IAD processes is governed by the maximalmodulus of the eigenvalues laying out of the peripheral spectrumof the smoothing matrix. The examined generators of Markovchains come from compartmental systems and cause that thetransition matrices under consideration may depend upon theappropriate stationary probability vectors. The nonlinearityrepresents further difficulties in computation.Ivo MarekSchool of Civil EngineeringCzech Institute of Technology, Praha, Czech [email protected]

MS 18. Preconditioning for PDE-constrainedoptimization - Part I of IITalk 1. Structural spectral properties of symmetric saddlepoint problemsSymmetric and indefinite block structured matrices often ariseafter the discretization of a large variety of application problems,where the block form stems from the presence of more than onepartial differential equation (PDE) in the problem, or from theimposition of some constraints, usually associated with PDEs.Structure-aware preconditioning strategies have emerged aswinning devises for efficiently and optimally solving theassociated large linear systems. In some relevant applications,the coefficient matrix shows a particular spectral symmetryaround the origin, which should be taken into account whenselecting both the iterative system solver and the mostappropriate preconditioner. In this talk we analyze in detail thissymmetry, and discuss its consequences in the solution of threemodel problems in optimal control, distributed time-harmonicparabolic control and distributed time-harmonic Stokes control.Valeria SimonciniDipartimento di MatematicaUniversità di Bologna, [email protected]

Wolfgang KrendlDoctoral Program Computational MathematicsJohannes Kepler University, Linz, [email protected]

Walter ZulehnerInstitute of Computational MathematicsJohannes Kepler University, 4040 Linz, [email protected]

Talk 2. Preconditioned iterative methods for Stokes andNavier-Stokes control problemsThe development of iterative solvers for PDE-constrainedoptimization problems is a subject of considerable recent interestin numerical analysis. In this talk, we consider the numericalsolution of two such problems, namely those of Stokes controland Navier-Stokes control. We describe the role of saddle pointtheory, mass matrix and Schur complement approximation,

multigrid routines, and commutator arguments, in theconstruction of solvers for these problems. We also discussissues involved with regularization terms, and, in the case ofNavier-Stokes control, the outer iteration employed. We displaynumerical results that demonstrate the effectiveness of oursolvers.John PearsonMathematical InstituteUniversity of [email protected]

Talk 3. Preconditioners for elliptic optimal control problemswith inequality constraintsIn this talk we consider optimal control problems with an ellipticboundary value problem as state equation. Based on recentresults for distributed elliptic optimal control problems withoutinequality constraints we present and discuss preconditioners forthe optimality system in the presence of additional controlconstraints or state constraints. The focus is on the performanceof these preconditioners within a Krylov subspace method withrespect to model and discretization parameters.A possible extension of the presented approach to optimalcontrol problems with other state equations, like the steady-stateStokes equations, is discussed.Walter ZulehnerInstitute of Computational MathematicsJohannes Kepler University, Linz, [email protected]

Markus KollmannDoctoral Program Computational MathematicsJohannes Kepler University, Linz, [email protected]

Talk 4. Nearly optimal block preconditioners for blocktwo-by-two linear systemsFor a class of block two-by-two systems of linear equations, weconstruct block preconditioning matrices and discuss theeigen-properties of the corresponding preconditioned matrices.The block preconditioners can be employed to accelerate theconvergence rates of Krylov subspace iteration methods such asMINRES and GMRES. Numerical experiments show that theblock preconditioners are feasible and effective when used insolving the block two-by-two linear systems arising from thefinite-element discretizations of a class of PDE-constrainedoptimization problems.Zhong-Zhi BaiInstitute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesP. O. Box 2719, Beijing 100190, [email protected]

MS 19. Matrices and graphs - Part I of IITalk 1. (0,1) matrices and the analysis of social networksIn the sociology literature, an m× n (0, 1) matrix is called anactor–event matrix. In many examples, the matrix A is uniquelydetermined by AAT , ATA, and the fact that A is (0, 1). In thistalk, we present a result on pairs of actor–event matrices that aredistinct but ‘close’, and yield the same AAT and ATA.Specifically, using techniques from combinatorial matrix theory,we characterise all pairs of (0, 1) matrices A1, A2 such thatA1A

T1 = A2A

T2 , A

T1 A1 = A

T2 A2, and the (0, 1,−1) matrix

A1−A2 has at most one 1 and one−1 in each row and column.


Steve KirklandHamilton InstituteNational University of Ireland [email protected]

Talk 2. Necessary and sufficient conditions for a HamiltoniangraphA graph is singular if the zero eigenvalue is in the spectrum of its0-1 adjacency matrix A. If an eigenvector belonging to the zeroeigenspace of A has no zero entries, then the singular graph issaid to be a core graph. A (κ, τ)-regular set is a subset of thevertices inducing a κ-regular subgraph such that every vertex notin the subset has τ neighbours in it. We consider the case whenκ = τ which relates to the eigenvalue zero under certainconditions. We show that if a regular graph has a (κ, κ)-regularset, then it is a core graph. By considering the walk matrix, wedevelop an algorithm to extract (κ, κ)-regular sets and formulatea necessary and sufficient condition for a graph to beHamiltonian.Irene ScirihaDept of Mathematics, Faculty of ScienceUniv. of [email protected]

Domingos Moreira CardosoDepartamento de MatemticaUniv. de [email protected]

Talk 3. On the eigenvalues of symmetric matrices associatedwith graphsLet G be a weighted graph of order n. It is known that λ1 ≥ d1and λ2 ≥ d3 where λi and di are the ith largest Laplacianeigenvalue and degree of G, respectively. For λ3 and smallereigenvalues we show that it is possible to construct a weightedgraph G of any order n such that λj < dn.To obtain these results we show that for every k ≥ 2 andn ≥ k + 1 there exists a weighted graph of order n whoseadjacency matrix has exactly k negative eigenvalues.This is done by obtaining some beautiful properties of the Schurcomplements of the adjacency matrix.Miriam FarberDepartment of [email protected]

Talk 4. An extension of the polytope of doubly stochasticmatricesWe consider a class of matrices whose row and column sumvectors are majorized by given vectors b and c, and whoseentries lie in the interval [0, 1]. This class generalizes the class ofdoubly stochastic matrices. We investigate the correspondingpolytope Ω(b|c) of such matrices. Main results include ageneralization of the Birkhoff - von Neumann theorem and acharacterization of the faces, including edges, of Ω(b|c).Richard A. BrualdiDepartment of MathematicsUniversity of [email protected]

Geir DahlCenter of Mathematics for ApplicationsDepartments of Mathematics and InformaticsUniversity of [email protected]

MS 20. Tensor based methods for high dimensionalproblems in scientific computing - Part I of II

Talk 1. Optimal a priori Tensor Decomposition for theSolution of High Dimensional ProblemsTensor-based methods are receiving a growing attention for theiruse in high dimensional applications in scientific computingwhere functions of multiple parameters have to beapproximated. These methods are based on the construction oftensor decompositions that provide approximate representationsof functions on adapted low dimensional reduced bases. Here,we propose algorithms that are able to directly construct anapproximation of optimal tensor decompositions with respect toa desired metric, without a priori information on the solution.Connections with optimal model reduction will be discussed.Anthony NouyLUNAM Université, GeM, UMR CNRS 6183, Ecole Centrale deNantes, Universit de Nantes, [email protected]

Talk 2. Application of the Proper Generalized Decomposition(PGD) to 3D cracked plates and estimation of thediscretization errorWe present a new numerical approach to solve cracked plates inan efficient way by obtaining a single solution in which thePoisson’s ratio ν and the plate thickness B are non-fixedparameters. With a single analysis, it is possible to obtain anumerical solution for a cracked plate problem that can beparticularized for any ν and B by simple post-processing, thusproviding an efficient tool for the numerical analysis of theseproblems. The method makes use of the Proper GeneralizedDecomposition (PGD). In this method, the sought displacementfield u(x, y, z, ν, B) is written as a series expansion of functionproducts. The formulation proposed here uses a 2Ddiscretization for the plane XY and a 1D discretization in theZ-direction. In addition, independent functions of ν and B areincluded in the tentative solution to be converged. An iterativeprocess is then carried out by which the necessary terms of theseries expansion are added in order to attain the requiredaccuracy. We have also implemented a recovery type errorestimator to evaluate the discretization error in energy norm bothin the XY plane (2D problem) and along the Z-direction (1Dproblem). The combination of both errors provides the localerror distribution that can be used to drive the h-adaptiverefinement.Eugenio GinerCentro Investigación Tecnologı́a de Vehı́culos - CITV, U. PolitècnicaValència, [email protected]

Chady GhnatiosEADS Chair at École Centrale de Nantes, [email protected]

Brice BognetEADS Chair at École Centrale de Nantes, [email protected]

Adrien LeygueEADS Chair at École Centrale de Nantes, [email protected]

Juan José RódenasCentro Investigación Tecnologı́a de Vehı́culos - CITV, U. PolitècnicaValència, [email protected]

F. Javier FuenmayorCentro Investigación Tecnologı́a de Vehı́culos - CITV, U. PolitècnicaValència, [email protected]

Francisco Chinesta


EADS Chair at École Centrale de Nantes, [email protected]

Talk 3. A tensor calculus approach for Bézier shapedeformationThe goal of our research is to obtain a computationally efficientdeformation of a parametric curve. This research is applied toengineering applications as, for example, mobile robotics andliquid composite moulding. A new technique was developed tomodify a Bézier curve by minimizing the changes of its shape.This shape modification is computed through a field of vectors,applying them on particular points of the Bézier curve (BézierShape Deformation, BSD). In these kinds of applications thecomputational cost is a critical issue because the parametriccurve must be modified in real time. Therefore, the original BSDalgorithm has been reformulated using algebra of tensors toreduce the computational time (Tensor-Bézier ShapeDeformation, T-BSD). While BSD grows exponentially, T-BSDgrows linearly. As a consequence, the Bézier curve is modifiedwith the lowest computational cost.Lucı́a HilarioDepartamento de Ciencias Fı́sicas, Matemáticas y de la Computación,Universidad CEU Cardenal Herrera, [email protected]

Nicolás MontésDepartamento de Ingenierı́a de la Edificación y Producción Industrial,Universidad CEU Cardenal Herrera ,[email protected]

Marta C. MoraDepartamento de Ingenierı́a Mecánica y Construcción, UniversitatJaume I , [email protected]

Antonio FalcóDepartamento de Economı́a Financiera y Contabilidad, Universidad deAlicante, [email protected]

Talk 4. Tensor approximation methods for parameteridentificationIn this talk we present methods for parameteridentification—here the coefficient fields of partial differentialequations—based on Bayesian procedures. As is well known,Bayes’s theorem for random variables (RVs) of finite va

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