About Me
I received my PhD in numerical mathematics at TU Wien. The main topics of my PhD thesis are Krylov techniques and approximations to the action of matrix exponentials. While my research mainly revolves around numerical analysis and computational mathematics, I also enjoy working on applications and development of numerical software. As a PhD student I was part of the doctoral college Unravelling Advanced 2D Materials (TU-D), which led to interdisciplinary collaborations focusing on time integration of quantum systems.
Some of my research collaborators are Winfried Auzinger (doctoral advisor), Florian Libisch (TU-D Speaker), Pranav Singh.
Research interests
Practical error estimates for Krylov approximations to the action of matrix exponentials. Adaptive Magnus-Krylov integrators. Geometric numerical integration. Time propagation of quantum systems. Rational best approximation to the imaginary exponential. Orthogonal polynomials, orthogonal rational functions, and related Gaussian quadrature formulae in the context of Krylov techniques. Variants of the near-best approximation property of rational Krylov methods.
Software
A Python package providing algorithms to approximate the unitary exponential function with a focus on unitary best approximations. Also available in the pypi package manager link. This package is still under development.
A Python package providing adaptive Magnus-Krylov and Krylov methods for time integration of Schrödinger-type equations. Also available in the pypi package manager link. This package is still under development.
A Python package providing some subroutines for Krylov propagators. The aim of this package is mostly to test f2py implementations using blas and lapack libraries in the pypi package manager, see also link, still under development.
Publication List
Preprints
- T. Jawecki. A review of the separation theorem of Chebyshev-Markov-Stieltjes for polynomial and some rational Krylov subspaces, 2022. preprint at https://arxiv.org/abs/2205.01535 pdf bib
- T. Jawecki and P. Singh. Unitary rational best approximations to the exponential function, 2023. preprint at https://arxiv.org/abs/2312.13809 pdf bib
Papers in Scientific Journals
- T. Jawecki and P. Singh. Unitarity of some barycentric rational approximants. IMA J. Numer. Anal., 44(4):2070–2089, 2024. doi:10.1093/imanum/drad066 pdf bib
- W. Auzinger, J. Dubois, K. Held, H. Hofstätter, T. Jawecki, A. Kauch, O. Koch, K. Kropielnicka, P. Singh, and C. Watzenböck. Efficient Magnus-type integrators for solar energy conversion in Hubbard models. J. Comput. Math. Data Sci., 2:100018, 2022. doi:10.1016/j.jcmds.2021.100018 pdf bib
- T. Jawecki. A study of defect-based error estimates for the Krylov approximation of phi-functions. Numer. Algorithms, 90(1):323–361, 2022. doi:10.1007/s11075-021-01190-x pdf bib
- W. Auzinger, T. Jawecki, O. Koch, P. Pukach, R. Stolyarchuk, and E.B. Weinmüller. Some aspects on [numerical] stability of evolution equations of stiff type; use of computer algebra. In 2021 IEEE XVII th International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH), pages 180–184, 2021. doi:10.1109/memstech53091.2021.9468055 bib
- C. Schattauer, L. Linhart, T. Fabian, T. Jawecki, W. Auzinger, and F. Libisch. Graphene quantum dot states near defects. Phys. Rev. B, 102:155430, 2020. doi:10.1103/PhysRevB.102.155430 bib
- T. Jawecki, W. Auzinger, and O. Koch. Computable upper error bounds for Krylov approximations to matrix exponentials and associated phi-functions. BIT, 60(1):157–197, 2020. doi:10.1007/s10543-019-00771-6 pdf bib
Theses
- T. Jawecki. Krylov techniques and approximations to the action of matrix exponentials. Ph.D thesis, TU Wien, Austria, 2022. doi:10.34726/hss.2022.45083 pdf bib
- T. Jawecki. Bifurcation analysis via numerical continuation for nonlinear fourth-order partial differential equations. Diploma thesis, TU Wien, 2017. doi:10.34726/hss.2017.42161 pdf bib