6 papers
Update to: Spectral sets: Numerical range and beyond
Michel Crouzeix, Anne Greenbaum
We use the results of Lorist and Schwenninger, {\em A solution to Crouzeix's conjecture}, arXiv:2608.03841v2, https://arxiv.org/abs/2608.03841, to update the 2019 paper of Crouzeix…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
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 w…
A New Proof that the Numerical Range is a Complete 2-Spectral Set for Weighted Shift Matrices
Michel Crouzeix, Anne Greenbaum
In this paper we give an alternative proof that the family of matrices studied by Daeshik Choi in A proof of Crouzeix's conjecture for a class of matrices, Linear Algebra and its A…
Stable algorithms for general linear systems by preconditioning the normal equations
Ethan N. Epperly, Anne Greenbaum, Yuji Nakatsukasa
This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned…
When is the Resolvent Like a Rank One Matrix?
Anne Greenbaum, Faranges Kyanfar, Abbas Salemi
For a square matrix , the resolvent of at a point is defined as . We consider the set of points where the relative differ…
Numerical bounds on the Crouzeix ratio for a class of matrices
Crouzeix Michel, Greenbaum Anne, Li Kenan
We provide numerical bounds on the Crouzeix ratiofor KLS matrices which have a line segment on the boundary of the numerical range. The Crouzeix ratio is the supremum over all…