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arXiv · 2602.05394

Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop

Noah Amsel·Yves Baumann·Paul Beckman·Peter Bürgisser·Chris Camaño·Tyler Chen·Edmond Chow·Anil Damle·Michal Derezinski·Mark Embree·Ethan N. Epperly·Robert Falgout·Mark Fornace·Anne Greenbaum·Chen Greif·Diana Halikias·Zhen Huang·Elias Jarlebring·Yiannis Koutis·Daniel Kressner·Rasmus Kyng·Jörg Liesen·Jackie Lok·Raphael A. Meyer·Yuji Nakatsukasa·Kate Pearce·Richard Peng·David Persson·Eliza Rebrova·Ryan Schneider·Rikhav Shah·Edgar Solomonik·Nikhil Srivastava·Alex Townsend·Robert J. Webber·Jess Williams
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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. (Updated to reflect the status of the open problems as of August 20, 2026.)

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Noah Amsel, Yves Baumann, Paul Beckman, Peter Bürgisser, Chris Camaño, Tyler Chen, Edmond Chow, Anil Damle, Michal Derezinski, Mark Embree, Ethan N. Epperly, Robert Falgout, Mark Fornace, Anne Greenbaum, Chen Greif, Diana Halikias, Zhen Huang, Elias Jarlebring, Yiannis Koutis, Daniel Kressner, Rasmus Kyng, Jörg Liesen, Jackie Lok, Raphael A. Meyer, Yuji Nakatsukasa, Kate Pearce, Richard Peng, David Persson, Eliza Rebrova, Ryan Schneider, Rikhav Shah, Edgar Solomonik, Nikhil Srivastava, Alex Townsend, Robert J. Webber, Jess Williams. 2026-02-05. Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop. https://arxiv.org/abs/2602.05394

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