Thomas Mach

University of Potsdam
Institute for Mathematics
Data Assimilation (Prof. Melina Freitag)
Campus Golm, Haus 29 (Office: 2.29.2.06)
Karl-Liebknecht-Str. 24-25
14476 Potsdam
Germany

E-Mail: mach(at)uni-potsdam.de
Office hours: currently by appointment only

Featured Publication

Core Chasing Algorithms for the Eigenvalue Problem, Fundamentals of Algorithms
J. L. Aurentz, T. Mach, L. Robol, R. Vandebril, D. S. Watkins, SIAM, 2018.


Research Interests

Numerical linear algebra for large or structured matrices, especially data analysis, inverse problems and eigenvalue algorithms, with tensor-structured, hierarchical, data-sparse, and rank structured matrices; unitary eigenvalue problems, polynomial root-finding, Krylov subspaces, inverse eigenvalue problems, and adaptive cross approximation.

Short CV

Selected Academic Services

Awards

  • SIAM Outstanding Paper Prize for J. L. Aurentz, T. Mach, R. Vandebril, and D. S. Watkins, Fast and Backward Stable Computation of Roots of Polynomials, SIAM Journal on Matrix Analysis and Applications, 36 (2015).

Publications

Books (1)

J. L. Aurentz, T. Mach, L. Robol, R. Vandebril, D. S. Watkins, SIAM, 2018.

Journal Articles (21)

T. Mach, L. Reichel, M. Van Barel, R. Vandebril, J. Comput. Appl. Math., 303 (2016), pp. 206‒217.

J. L. Aurentz, T. Mach, R. Vandebril, D. S. Watkins, Electron. Trans. Numer. Anal., 44 (2015), pp. 327‒341.

J. L. Aurentz, T. Mach, R. Vandebril, D. S. Watkins, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 942‒973. SIAM Outstanding Paper Prize.

T. Mach, R. Vandebril, SIAM J. Matrix Anal. Appl., 35 (2014), 559‒579.

T. Mach, M. Pranić, R. Vandebril, Electron. Trans. Numer. Anal., 40 (2013), pp. 414‒435.

P. Benner, T. Mach, Linear Algebra Appl., 439 (2013), pp. 1150‒1166.

P. Benner, T. Mach, Numer. Linear Algebra Appl., 20 (2013), pp. 150‒166.

P. Benner, T. Mach, SIAM J. Sci. Comput., 34 (2012), pp. A485‒A496.

P. Benner, T. Mach, Computing, 88 (2010), pp. 111‒129.

Conference Proceedings (8)

  1. A note on companion pencil, J. L. Aurentz, T. Mach, R. Vandebril, D. S. Watkins, 658 (2016) AMS Contemporary Mathematics, pp. 91‒102.

  2. Extended Hamiltonian Hessenberg matrices arise in projection based model order reduction, M. Ferranti, T. Mach, R. Vandebril, in Proceedings in Applied Mathematics and Mechanics, 15 (2015), pp. 583‒584.

  3. A numerical example showing that deflations based on rotations leads to higher relative accuracy, T. Mach, R. Vandebril, in Proceedings in Applied Mathematics and Mechanics, 14 (2014), pp. 823‒824.

  4. Computing inner eigenvalues of matrices in tensor train matrix format, T. Mach, in ENUMATH 2011 Proceedings Volume (2013), pp. 781‒789.

  5. How competitive is the ADI for tensor structured equations, T. Mach, J. Saak, in Proceedings in Applied Mathematics and Mechanics, 12 (2012), pp. 635‒634.

  6. Locally optimal block preconditioned conjugate gradient method for hierarchical matrices, P. Benner, T. Mach, in Proceedings in Applied Mathematics and Mechanics, 11 (2011), pp. 741‒742.

  7. Computing the eigenvalues of hierarchical matrices by LR-Cholesky transformations, P. Benner, T. Mach, in Mathematisches Forschungsinstitut Oberwolfach, Report No. 37/2009 (2009), pp. 325‒328.

  8. Control of a shell and tube heat exchanger, in Proceedings of the European Student Workshop on Mathematical Modelling in Industry 2005 (2006), pp. 117‒134.

Thesis (2)

Seminars and Presentations at Conferences

If you are interested in my slides of a specific talk below, please email (mach(at)uni-potsdam.de) me.

  • 27‒29 May 2019, ETNA25 Conference on Recent Advances in Scientific Computing, Santa Margherita di Pula, Italy,
    Organization of a minisymposium on Krylov Subspace Methods and Their Applications (together with Marc Van Barel) and,
    talk in minisymposium Adaptive Cross Approximation for Ill-Posed Problems

  • 04‒08 May 2018, SIAM Conference on Applied Linear Algebra, Hong Kong Baptist University,
    Organization of a minisymposium on Recent applications of rank structures in matrix analysis (together with Stefano Massei and Leonardo Robol) and,
    talk in minisymposium Adaptive Cross Approximation for Ill-Posed Problems

  • 19‒23 Mar 2018, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics, Munich,
    contribute talk Fast and backward stable computations of roots of polynomials ‒ backward error analysis

  • 24‒28 Jul 2017, 21th Conference of the International Linear Algebra Society (ILAS), Ames, Iowa,
    talk in minisymposium Inverse Free Rational Krylov Subspaces for Computing Matrix Functions

  • 18‒23 Jun 2017, 20th Householder Symposium on Numerical Linear Algebra Society, Blacksburg, Virginia,
    poster Computing the roots of polynomials in Chebyshev basis via the Cayley transform

  • 1o Oct 2016, Seminar talk at KU Leuven, On rotations and (rational) Krylov subspaces

  • 11‒15 Jul 2016, 20th Conference of the International Linear Algebra Society (ILAS), Leuven, Belgium,
    member of the organizing team
    talk in minisymposium Computing roots of polynomials in Chebyshev basis via the Cayley transform

  • 07 Apr 2016, Seminar talk at KTH Stockholm, On rotations and (rational) Krylov subspaces

  • 26‒30 Oct 2015, SIAM Conference on Applied Linear Algebra, Atlanta, Georgia, USA,
    talk in minisymposium Fast and stable computation of the roots of polynomials

  • 09‒10 Jul 2015, GAMM Workshop on Applied and Numerical Linear Algebra 2015, Magdeburg, Germany,
    contributed talk An extended Hamiltonian QR algorithm

  • 8‒12 Sept 2014, Structured Numerical Linear and Multilinear Algebra: Analysis, Algorithms, and Applications, Kalamata, Greece,invitation only, Fast and stable computation of the roots of polynomials

  • 6‒9 Aug 2014, 19th Conference of the International Linear Algebra Society (ILAS), Seoul, Korea,contributed talk Computing Approximate Rational Krylov Subspaces Without Explicit Inversion

  • 25‒28 Jun 2014, Workshop on Computational Methods in Optimization and System and Control Theory, Schloss Ringberg, Germany,invitation only, On rotations and (rational) Krylov subspaces

  • 2‒5 Jun 2014, 10th International Workshop on Accurate Solution of Eigenvalue Problems, Dubrovnik, Croatia,contributed talk On Deflations in Extended QR Algorithms

  • 10‒14 Mar 2014, 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics, FAU Erlangen, Germany,
    contributed talk On Deflations in Extended QR Algorithms

  • 09‒10 Sept 2013, GAMM Workshop on Applied and Numerical Linear Algebra 2013, Wuppertal, Germany,
    contributed talk On Deflations in Extended QR Algorithms

  • 24‒26 Jun 2013, Numerical Analysis and Scientific Computation with Applications (NASCA13), Calais, France,
    contributed talk Inverse eigenvalue problems linked to rational Arnoldi, and rational (non)symmetric Lanczos

  • 3‒7 Jun 2013, 18th Conference of the International Linear Algebra Society (ILAS), Providence, Rhode Island, USA,
    talk in minisymposium Inverse eigenvalue problems linked to rational Arnoldi, and rational (non)symmetric Lanczos

  • 11 Apr 2013, Seminar talk at J. J. Strossmayer University of Osijek, Computing Approximate Extended Krylov Subspaces without Explicit Inversion

  • 4‒7 Jun 2012,9th International Workshop on Accurate Solution of Eigenvalue Problems, Napa Valley, California, USA,
    contributed talk Eigenvalues of Symmetric Hierarchical Matrices

  • 26‒30 Mar 2012,83rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, TU Darmstadt, Germany,
    contributed talk ADI for Tensor Structured Equation

  • 21‒22 Nov 2011, Workshop on Matrix Equations and Tensor Techniques, RWTH Aachen, Germany,
    contributed talk ADI for Tensor Structured Equation

  • 22‒23 Sept 2011, GAMM Workshop Applied and Numerical Linear Algebra, University of Bremen, Germany,
    contributed talk Computing Inner Eigenvalues of Matrices in Tensor Train Format

  • 5‒9 Sept 2011, ENUMATH Conference 2011, University of Leicester, United Kingdom,
    contributed talk Computing Inner Eigenvalues of Matrices in Tensor Train Format

  • 22‒26 Aug 2011, 17th Conference of the International Linear Algebra Society (ILAS), TU Braunschweig, Germany,
    contributed talk Why the LR Cholesky algorithm does not work for hierarchical matrices

  • 26‒30 Jun 2011, 4th Workshop on High-Dimensional Approximation, University of Bonn, Germany

  • 26‒30 Mar 2011, 82nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, TU Graz, Austria,
    contributed talk Preconditioned Inverse Iteration for Hierarchical Matrices

  • 27‒29 Sept 2010, 23rd Chemnitz FEM Symposium 2010, TU Chemnitz, Germany, contributed talk Preconditioned Inverse Iteration for H-Matrices

  • 28 Jun‒01 Jul 2010, 8th International Workshop on Accurate Solution of Eigenvalue Problems, TU Berlin, Germany, poster Slicing the Spectrum of Symmetric Hl-Matrices

  • 26‒29 Oct 2009, SIAM Conference on Applied Linear Algebra, Monterey, California, USA,
    contributed talk On the QR Decomposition of H-Matrices

  • 10‒11 Sept 2009, GAMM Workshop Applied and Numerical Linear Algebra, ETH Zurich, Switzerland,
    contributed talk LR-Cholesky Transformations for Hierarchical Matrices and other Algorithms to Compute the Eigenvalues of Hierarchical Matrices