Estimating the numerical range with a Krylov subspace
Numerical Analysis
2024-12-02 v1 Numerical Analysis
Abstract
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix. In contrast to prior results, which often depend on the gaps between eigenvalues, our estimates depend only on the dimensions of the matrix and Krylov subspace, and the conditioning of the eigenbasis of the matrix. In addition, we provide nearly matching lower bounds for our estimates, illustrating the tightness of our arguments.
Cite
@article{arxiv.2411.19165,
title = {Estimating the numerical range with a Krylov subspace},
author = {Cecilia Chen and John Urschel},
journal= {arXiv preprint arXiv:2411.19165},
year = {2024}
}