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06/29/2023
Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm
Given an n by n matrix A and an n-vector b, along with a rational functi...
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03/06/2023
Near-Optimality Guarantees for Approximating Rational Matrix Functions by the Lanczos Method
We study the Lanczos method for approximating the action of a symmetric ...
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03/03/2023
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices
We study the GMRES algorithm applied to linear systems of equations invo...
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02/10/2023
K-Spectral Sets
We use results in [M. Crouzeix and A. Greenbaum,Spectral sets: numerical...
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02/23/2022
Low-memory Krylov subspace methods for optimal rational matrix function approximation
We describe a Lanczos-based algorithm for approximating the product of a...
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06/17/2021
Error bounds for Lanczos-based matrix function approximation
We analyze the Lanczos method for matrix function approximation (Lanczos...
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06/08/2020
Crouzeix's Conjecture and related problems
In this paper, we establish several results related to Crouzeix's conjec...
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05/14/2019
On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic
We consider three mathematically equivalent variants of the conjugate gr...
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03/02/2019