# Thomas Mach

Postdoc in Data Assimilation

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

Since 2020: Postdoc, Institute for Mathematics for Mathematics, University Potsdam, Germany

2018—2019: Postdoc, Department of Mathematical Sciences, Kent State University, Ohio

2016—2018: Assistant Professor, School of Science and Technology, Nazarbayev University, Kazakhstan

2012—2016: Postdoc, Department Computer Science, KU Leuven, Belgium

2010—2012: PhD student, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

2008—2010: PhD student, TU Chemnitz, Germany

### Selected Academic Services

Associate Editor Electronic Transactions on Numerical Analysis

Member of the organizing team for the ILAS conference 2016 in Leuven, Beligum

### 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)

N. Eshghi, T. Mach, L. Reichel, J. Comput. Appl. Math., 2021, in press.

D. Camps, T. Mach, R. Vandebril, D. S. Watkins, Electron. Trans. Numer. Anal., 52 (2020), pp. 480‒508.

T. Mach, T. Steel, R. Vandebril, D. S. Watkins, Vietnam J. Math., 48 (2020), pp. 679‒701 .

J. L. Aurentz, T. Mach, L. Robol, R. Vandebril, D. S. Watkins, Math. Comp., 88 (2019), pp. 313‒347.

J. L. Aurentz, T. Mach, L. Robol, R. Vandebril, D. S. Watkins, SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1245‒1269.

J. L. Aurentz, T. Mach, R. Vandebril, D. S. Watkins, Electron. Trans. Numer. Anal., 46 (2017), pp. 447‒459.

M. Ferranti, B. Iannazzo, T. Mach, R. Vandebril, Calcolo, 54 (2017), pp. 1097‒1120.

M. Ferranti, B. Iannazzo, T. Mach, R. Vandebril, Calcolo, 54 (2017), pp. 423‒453.

C. Jagels, T. Mach, L. Reichel, R. Vandebril, Linear Algebra Appl., 510 (2016), pp. 291‒310.

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. Van Barel, R. Vandebril, J. Comput. Appl. Math., 272 (2014), pp. 377‒398.

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.

### Conference Proceedings (8)

**A note on companion pencil**, J. L. Aurentz, T. Mach, R. Vandebril, D. S. Watkins, 658 (2016) AMS Contemporary Mathematics, pp. 91‒102.**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.**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.**Computing inner eigenvalues of matrices in tensor train matrix format**, T. Mach, in ENUMATH 2011 Proceedings Volume (2013), pp. 781‒789.**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.**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.**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.**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)

Dissertation, TU Chemnitz, April 2012, 175 pages. (on Google Books)

Diplomarbeit, TU Chemnitz, May 2008, 71 pages.

### 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 Problems04‒08 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 Problems19‒23 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 analysis24‒28 Jul 2017, 21th Conference of the International Linear Algebra Society (ILAS), Ames, Iowa,

talk in minisymposium Inverse Free Rational Krylov Subspaces for Computing Matrix Functions18‒23 Jun 2017, 20th Householder Symposium on Numerical Linear Algebra Society, Blacksburg, Virginia,

poster Computing the roots of polynomials in Chebyshev basis via the Cayley transform1o 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 transform07 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 polynomials09‒10 Jul 2015, GAMM Workshop on Applied and Numerical Linear Algebra 2015, Magdeburg, Germany,

contributed talk An extended Hamiltonian QR algorithm8‒12 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 Algorithms09‒10 Sept 2013, GAMM Workshop on Applied and Numerical Linear Algebra 2013, Wuppertal, Germany,

contributed talk On Deflations in Extended QR Algorithms24‒26 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 Lanczos3‒7 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 Lanczos11 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 Matrices26‒30 Mar 2012,83rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, TU Darmstadt, Germany,

contributed talk ADI for Tensor Structured Equation21‒22 Nov 2011, Workshop on Matrix Equations and Tensor Techniques, RWTH Aachen, Germany,

contributed talk ADI for Tensor Structured Equation22‒23 Sept 2011, GAMM Workshop Applied and Numerical Linear Algebra, University of Bremen, Germany,

contributed talk Computing Inner Eigenvalues of Matrices in Tensor Train Format5‒9 Sept 2011, ENUMATH Conference 2011, University of Leicester, United Kingdom,

contributed talk Computing Inner Eigenvalues of Matrices in Tensor Train Format22‒26 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 matrices26‒30 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 Matrices27‒29 Sept 2010, 23rd Chemnitz FEM Symposium 2010, TU Chemnitz, Germany, contributed talk Preconditioned Inverse Iteration for

**H**-Matrices28 Jun‒01 Jul 2010, 8th International Workshop on Accurate Solution of Eigenvalue Problems, TU Berlin, Germany, poster Slicing the Spectrum of Symmetric

**H**l-Matrices26‒29 Oct 2009, SIAM Conference on Applied Linear Algebra, Monterey, California, USA,

contributed talk On the QR Decomposition of H-Matrices10‒11 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