Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Abstract
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was organized at the Simons Institute for the Theory of Computing program on Complexity and Linear Algebra in Fall 2025. The complexity and numerical solution of linear algebra problems is a crosscutting area between theoretical computer science and numerical analysis. The value of the particular problem formulations here is that they were produced via discussions between researchers from both groups. The open questions are organized in five categories: iterative solvers for linear systems, eigenvalue computation, low-rank approximation, randomized sketching, and other areas including tensors, quantum systems, and matrix functions.
Cite
@article{arxiv.2602.05394,
title = {Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop},
author = {Noah Amsel and Yves Baumann and Paul Beckman and Peter Bürgisser and Chris Camaño and Tyler Chen and Edmond Chow and Anil Damle and Michal Derezinski and Mark Embree and Ethan N. Epperly and Robert Falgout and Mark Fornace and Anne Greenbaum and Chen Greif and Diana Halikias and Zhen Huang and Elias Jarlebring and Yiannis Koutis and Daniel Kressner and Rasmus Kyng and Jörg Liesen and Jackie Lok and Raphael A. Meyer and Yuji Nakatsukasa and Kate Pearce and Richard Peng and David Persson and Eliza Rebrova and Ryan Schneider and Rikhav Shah and Edgar Solomonik and Nikhil Srivastava and Alex Townsend and Robert J. Webber and Jess Williams},
journal= {arXiv preprint arXiv:2602.05394},
year = {2026}
}
Comments
57 pages; no changes to content (source cleanup only)