# Thomas Mach

Thomas joined the Department of Mathematics in September 2016. Thomas Mach’s research interests lie in *numerical linear algebra*. He focuses on structured preserving and structure exploiting algorithms. Numerical linear algebra algorithms can become orders of magnitude faster by exploiting the available structure in matrices. Structure preservation on the other hand can also be expensive, but necessary to preserve physical properties. Some years ago, Thomas investigated the solution of boundary element and eigenvalue problems with hierarchical matrices. Recently, he has worked on backward stable algorithm for the unitary and Hamiltonian eigenvalue problem, and for polynomial root finding. Currently, his research further involves inverse eigenvalue problem, adaptive cross approximation, inverse integral equations, and polynomial and structured eigenvalue problems.

Thomas holds a PhD degree from the University of Chemnitz, Germany, where he also obtained an undergraduate degree. During his PhD he worked for the Max Planck Institute for Dynamics of Complex Technical Systems. The last four years Thomas worked as a postdoctoral researcher in Raf Vandebril’s group at KU Leuven, Belgium.

## Featured Publication

Recently the paper Convergence rates for inverse-free rational approximation of matrix functions joint work with Carl Jagels, Thomas Mach, Lothar Reichel, and Raf Vandebril got accepted for publication in *Linear Algebra and Its Applications* (DOI: 10.1016/j.laa.2016.08.029). The paper investigates the convergence behavior of the method developed in *Computing Approximate Extended Krylov Subspaces without Explicit Inversion* and *Computing Approximate (Block) Rational Krylov Subspaces without Explicit Inversion with Extensions to Symmetric Matrices* by Thomas Mach, Miroslav Pranić, and Raf Vandebril.

## Research Interest

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

## Short CV

- 2016—2019: 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