Numerical linear algebra
f(A)b, i.e., the computation of a matrix function times a vector
Krylov subspace methods
Backward stability analysis
FAIR data principles and open access in science
Publications, pre-prints, and technical reports
As much as legally possible, I have tried to make all my work open access. Please try OAButton if you are having trouble finding a paper.
Kathryn Lund and Marcel Schweitzer. The Fréchet derivative of the tensor t-function. arXiv:2302.09687, 2023. Software.
Kathryn Lund. Adaptively restarted block Krylov subspace methods with low-synchronization skeletons. Numerical Algorithms, 2022. Pre-print. Software.
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. Software.
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. Pre-print. Software.
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. Pre-print. Software.
Stefan Güttel, Daniel Kressner, and Kathryn Lund. Limited-memory polynomial methods for large-scale matrix functions. GAMM - Mitteilungen, 43(3), e202000019, 2020. Pre-print.
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. Open Access. Software.
Kathryn Lund. The tensor t-function: a definition for functions of third-order tensors. Numerical Linear Algebra with Applications, 27 (3), e2288, 2020. Pre-print. Software, 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. Software.
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. Open Access.
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.
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.
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.