# 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.

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.