Research
Interests
My work lies at the intersection of numerical linear and multilinear algebra, scientific computing, and high-performance computing (HPC). I am particularly interested in
f(A)b: functions of large, sparse matrices and their action on a vector
Fréchet derivatives
Bivariate matrix functions
Matrix equations
Tensor t-product
Krylov subspace methods, especially their scalability via communication-reducing techniques for HPC
Rounding-error analysis
FAIR data principles in scientific software
Open access in scientific publishing
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.
Erin Carson, Yuxin Ma, Kathryn Lund, and Eda Oktay. Reorthogonalized Pythagorean variants of block classical Gram-Schmidt. SIAM Journal on Matrix Analysis and Applications, 46(1), pp. 310--340, 2025. Pre-print. Software.
Erin Carson, Yuxin Ma, Kathryn Lund, and Eda Oktay. On the loss of orthogonality in low-synchronization variants of reorthogonalized block classical Gram-Schmidt. Technical Report arXiv:2408.10109, 2024. Software.
Kathryn Lund and Davide Palitta. Low-rank-modified Galerkin methods for the Lyapunov equation. Electronic Transactions on Numerical Analysis, Vol. 62, pp. 1--21, 2024. Software.
Massimiliano Fasi, Stéphane Gaudreault, Kathryn Lund, and Marcel Schweitzer. Challenges in computing matrix functions. Technical Report arXiv:2401.16132, Submitted, 2024.
Peter Benner, Kathryn Lund, and Jens Saak. Towards a Benchmark Framework for Model Order Reduction in the Mathematical Research Data Initiative (MaRDI). Proceedings in Applied Mathematics & Mechanics, pp. e202300147, 2023. Pre-print. Software.
Kathryn Lund and Marcel Schweitzer. The Fréchet derivative of the tensor t-function. Calcolo, Vol 60(35). 2023. Pre-print. Software.
Kathryn Lund. Adaptively restarted block Krylov subspace methods with low-synchronization skeletons. Numerical Algorithms, Vol. 93, 731--764, 2023. Pre-print. Software.
Erin C. 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, 2022. 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 C. 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.
block_Krylov_Luminy2019.pdf
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.