3 papers
math.FA2025
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…
math.NA2025
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…
math.NA2025
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…