Research

Interests

Numerical linear algebra
f(A)b, i.e., the computation of a matrix function times a vector
Krylov subspace methods
High-performance computing
Backward stability analysis
FAIR data principles and open access in science

Wuppertal, DE, 2016

Publications, pre-prints, and technical reports

Kathryn Lund: Adaptively restarted block Krylov subspace methods with low-synchronization skeletons, Numerical Algorithms, 2022. For more accurate formatting of the algorithms, please see the arXiv version. Software hosted on the CSC Gitlab.
Erin Carson, Kathryn Lund, Miroslav Rozložník, and Stephan Thomas: Block Gram-Schmidt algorithms and their stability properties, Linear Algebra and its Applications, Vol. 628, pp. 150-195, 2021. Pre-print available here. Associated software hosted on Github.

Errata: Algorithms 5 & 7 have a typo in the last couple lines, where the dimension s is written. It should be p. The code is written correctly.

Erin Carson, Kathryn Lund, and Miroslav Rozložník: The stability of block variants of classical Gram-Schmidt. SIAM Journal on Matrix Analysis and Applications, 42(3), pp. 1365--1380, 2021. Associated software hosted on Github. Pre-print available here.
Daniel Kressner, Kathryn Lund, Stefano Massei, and Davide Palitta. Compress-and-restart block Krylov subspace methods for Sylvester matrix equations. Numerical Linear Algebra with Applications. 28(1), e2339, 2021. Associated software can be found on Gitlab. The arXiv version may be more legible for some readers.
Stefan Güttel, Daniel Kressner, and Kathryn Lund. Limited-memory polynomial methods for large-scale matrix functions. GAMM - Mitteilungen, 43(3), e202000019, 2020. The arXiv version may be more legible for some readers.
Andreas Frommer, Kathryn Lund, and Daniel B. Szyld, Block Krylov subspace methods for functions of matrices II: Modified block FOM, SIAM Journal on Matrix Analysis and Applications, 41(2), pp. 804--837, 2020. The associated software can be found on Gitlab.
Kathryn Lund, The tensor t-function: a definition for functions of third-order tensors, Numerical Linear Algebra with Applications, 27 (3), e2288, 2020. The published version is identical in terms of content to the latest arXiv version. The associated software can be found on Gitlab, as a test script of B(FOM)^2.
Andreas Frommer, Kathryn Lund, and Daniel B. Szyld, Block Krylov subspace methods for functions of matrices, Electronic Transactions on Numerical Analysis, Vol. 47, pp. 100--126, 2017. The associated software can be found on Gitlab.
Andreas Frommer, Kathryn Lund, Marcel Schweitzer, and Daniel B. Szyld, The Radau-Lanczos method for matrix functions, SIAM Journal on Matrix Analysis and Applications, 38(3), pp. 710--732, 2017.

block_Krylov_Luminy2019.pdf

For an overview of my thesis and related papers, check out the poster I presented at a recent conference at CIRM in Luminy, France. The format is modified from the "better poster" LaTeX template. Feel free to contact me for my TeX files.

Berlin, DE, 2015

Past work and interests

Train schedule optimization

In the summer of 2015, I spent two months at the Zuse Institut Berlin working on train schedule optimization as a part of GRIPS (Graduate-level Research in Industrial Projects for Students), a program coordinated in part by the Institute for Pure and Applied Mathematics. A summary of my team's work is provided as a technical report.

Traffic modeling

As an undergraduate at Temple University, I researched traffic modeling under Benjamin Seibold. I presented my work, Five Dimensions of Traffic as a poster for the 2012 Undergraduate Research Symposium at Temple University and also for Mid-Atlantic Numerical Analysis Day 2012.