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MAT TRIAD 2019 Book of Abstracts MAT TRIAD 2019 International Conference on Matrix Analysis and its Applications Book of Abstracts September 8 13, 2019 Liblice, Czech Republic MAT TRIAD 2019 is organized and supported by MAT TRIAD 2019 Edited by Jan Bok, Computer Science Institute of Charles University, Prague David Hartman, Institute of Computer Science, Czech Academy of Sciences, Prague Milan Hladík, Department of Applied Mathematics, Charles University, Prague Miroslav Rozloºník, Institute of Mathematics, Czech Academy of Sciences, Prague Published as IUUK-ITI Series 2019-676ø by Institute for Theoretical Computer Science, Faculty of Mathematics and Physics, Charles University Malostranské nám. 25, 118 00 Prague 1, Czech Republic Published by MATFYZPRESS, Publishing House of the Faculty of Mathematics and Physics, Charles University in Prague Sokolovská 83, 186 75 Prague 8, Czech Republic Cover art c J. Na£eradský, J. Ne²et°il c Jan Bok, David Hartman, Milan Hladík, Miroslav Rozloºník (eds.) c MATFYZPRESS, Publishing House of the Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic, 2019 i Preface This volume contains the Book of abstracts of the 8th International Conference on Matrix Anal- ysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers in a variety of aspects of matrix analysis and its interdisciplinary applications to meet and share interests and ideas. The conference topics include matrix and operator theory and computation, spectral problems, applications of linear algebra in statistics, statistical models, matrices and graphs as well as combinatorial matrix theory and others. The goal of this event is to encourage further growth of matrix analysis research including its possible extension to other elds and domains. MAT TRIAD 2019 is a registered as satellite meeting of ICIAM 2019, The International Congress on Industrial and Applied • Mathematics, to be held at Valencia, Spain, July 15-19, 2019, http://iciam2019.org/, ILAS-Endorsed Meeting, https://www.ilasic.org/misc/meetings.html. • MAT TRIAD 2019 in Liblice in Czech Republic is organized based on the successful concept of previous MAT TRIAD editions, which are held biannually since 2005. The conference is scheduled for ve days with a series of invited lectures by leading experts in their eld. The invited speakers are: Dario Bini (University of Pisa) • Mirjam Dür (University of Augsburg) • Arnold Neumaier (University of Vienna) • Martin Stoll (Technical University of Chemnitz) • Two of the invited speakers serve as lectures: Shmuel Friedland (University of Illinois) - the Hans Schneider ILAS Lecturer • Zden¥k Strako² (Charles University) • Two recipients of the Young Scientists Awards from MAT TRIAD 2017, which took place in B¦dlewo, are also invited to give their lecture: Álvaro Barreras (Universidad Internacional de La Rioja) • Ryo Tabata (National Institute of Technology) • ii There are four special sessions organized: Total positivity • organiser: Mohammad Adm, Palestine Polytechnic University, Hebron & Jürgen Garlo, University of Applied Sciences and University of Konstanz Tropical matrix algebra and its applications • organiser: Aljo²a Peperko, University of Ljubljana, Slovenia & Sergei Sergeev, University of Birmingham, UK Recent developments of veried numerical computations • organizer: Takeshi Ogita, Tokyo Woman's Christian University & Siegfried M. Rump, Ham- burg University of Technology Interval matrices • organiser: Milan Hladík, Charles University, Prague First, we wish to thank International Linear Algebra Society and RSJ Foundation, to make the conference possible as well as other supporters and sponsors. We thank the members of scientic committee for their work and feedback on the event and to members of local organizing committee for their cooperation and help with necessary organizational tasks. We want to thank all invited speakers for accepting invitations and preparations of their presentations as well as all participants of the conference to make the event possible. We wish them rich time and fruitful discussions during MAT TRIAD 2019 in Liblice. Miroslav Rozloºník, Milan Hladík The nal program is available at https://mattriad.math.cas.cz/ Scientic Committee Tomasz Szulc, chair, Adam Mickiewicz University, Pozna«, Poland Natália Bebiano, University of Coimbra, Coimbra, Portugal Ljiljana Cvetkovi£, University of Novi Sad, Serbia Heike Faÿbender, Technische Universität Braunschweig, Germany Simo Puntanen, University of Tampere, Finland Local Organizing Committee Miroslav Rozloºník, Institute of Mathematics, Czech Academy of Sciences, Prague Milan Hladík, Department of Applied Mathematics, Charles University, Prague Hana Bílková, Institute of Mathematics and Institute of Computer Science, Czech Academy of Sciences Jan Bok, Computer Science Institute of Charles University, Prague David Hartman, Department of Applied Mathematics, Charles University, Prague and In- stitute of Computer Science, Czech Academy of Sciences, Prague Jaroslav Horá£ek, Department of Applied Mathematics, Charles University, Prague Miroslav T·ma, Department of Numerical Mathematics, Charles University, Prague Petr Tichý, Department of Numerical Mathematics, Charles University, Prague iii Contents Invited talks 1 Álvaro Barreras, Juan Manuel Peña: Tridiagonal inverses of tridiagonal M-matrices and related pentadiagonal matrices 2 Dario A. Bini: Solving matrix equations encountered in stochastic processes: an algorithmic analysis 4 Mirjam Dür: Copositive optimization and completely positive matrix factorization . 6 Shmuel Friedland: The Collatz-Wielandt quotient for pairs of nonnegative operators .......... 9 Arnold Neumaier: Condence intervals for large-scale linear least squares solutions . 11 Martin Stoll: From PDEs to data science: an adventure with the graph Laplacian . 12 Zden¥k Strako²: Operator preconditioning, spectral information and convergence behavior of Krylov subspace methods .................................... 13 Ryo Tabata: Immanants and symmetric functions ......................... 15 Special sessions 17 Total positivitity 18 Rola Alseidi, Michael Margaliot, Jürgen Garlo: On the spectral properties of nonsingular matrices that are strictly sign-regular for some order with applications to totally positive discrete-time systems . 19 Kanae Akaiwa, Kazuki Maeda: An inverse eigenvalue problem for pentadiagonal oscillatory matrices . 21 Jürgen Garlo, Mohammad Adm, Khawla Al Muhtaseb, and Ayed AbedelGhani: Relaxing the nonsingularity assumption for intervals of totally nonnegative matrices 23 Apoorva Khare: Total positivity preservers ............................... 24 iv Plamen Koev: Accurate eigenvalues and zero Jordan blocks of (singular) sign-regular matrices . 26 Olga Kushel: Totally positive matrices in the theory of robust spectral clustering . 28 Ana Marco, José-Javier Martínez, Raquel Viaña: Totally positive h-Bernstein bases, bidiagonal decomposition, and applications . 30 J. Delgado, H. Orera, J. M. Peña: On accurate computations with subclasses of totally positive matrices . 32 Alexander Dyachenko, Mikhail Tyaglov: On the number of zeroes and poles of functions generating Pólya frequency sequences 33 Tropical matrix algebra and its applications 35 Marianne Akian, Stéphane Gaubert, Louis Rowen: Linear algebra and convexity over symmetrized semirings, hyperelds and systems 36 Nikolai Krivulin: Complete solution of tropical vector inequalities using matrix sparsication . 38 Nicola Guglielmi, Oliver Mason, Aisling McGlinchey, Fabian Wirth: On Barabanov norms and subeigencones for max algebraic inclusions, and opacity for systems over the max algebra ............................ 39 Zur Izhakian, Glenn Merlet: Tropical matrices: ranks, powers and semigroup identities . 41 Stéphane Gaubert, Adi Niv: Tropical planar networks ................................ 43 Aljo²a Peperko, Vladimir Müller: The Bonsall and lower cone spectral radius of suprema preserving mappings and approximate point spectrum .............................. 46 Artur Pi¦kosz: Some geometry of the SMPA .............................. 48 María Jesús de la Puente: QuasiEuclidean classication of maximal alcoved convex polyhedra . 50 Amnon Rosenmann, Franz Lehner, Aljo²a Peperko: Polynomial convolutions in max-plus algebra ..................... 53 Louis Rowen: Geometry and linear algebra on systems ........................ 55 Any Muanalifah, Daniel Jones, Serge¨Sergeev: Cryptography using tropical matrix algebra ...................... 57 Karel Zimmermann: Two-sided equation (max,+)/(min,+)-systems .................... 59 Recent developments of veried numerical computations 62 Siegfried M. Rump, Marko Lange: Veried inclusion of a nearby matrix of specied rank deciency . 63 Atsushi Minamihata, Takeshi Ogita, Shin'ichi Oishi: A note on verication methods for sparse non-symmetric linear systems . 65 v Takeshi Ogita, Kengo Nakajima: Accurate and veried solutions of large sparse linear systems arising from 3D Pois- son equation ....................................... 67 Denis Chaykin, Christian Jansson, Frerich Keil, Marko Lange, Kai Torben Ohlhus, Siegfried M. Rump: Rigorous results in electronic structure calculations . 69 Katsuhisa Ozaki, Takeshi Ogita: Error-free transformation of a product of three matrices and its applications . 71 Florian Bünger, Siegfried M. Rump: Gershgorin circles and the determinant of real or complex matrices . 73 Siegfried M. Rump: Sharp inclusions of the determinant of real or complex, point or interval matrices . 75
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