English

How well-conditioned can the eigenvalue problem be?

Numerical Analysis 2021-05-18 v1 Numerical Analysis Classical Analysis and ODEs

Abstract

The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalue computations? In this note we answer this question with exact first order asymptotic.

Cite

@article{arxiv.2105.07922,
  title  = {How well-conditioned can the eigenvalue problem be?},
  author = {Carlos Beltrán and Laurent Bétermin and Peter Grabner and Stefan Steinerberger},
  journal= {arXiv preprint arXiv:2105.07922},
  year   = {2021}
}

Comments

6 pages, 2 figures

R2 v1 2026-06-24T02:11:12.895Z