How well-conditioned can the eigenvalue problem be?

Carlos Beltrán; Laurent Bétermin; Peter Grabner; Stefan Steinerberger

doi:10.1090/mcom/3706

How well-conditioned can the eigenvalue problem be?

Carlos Beltrán, Laurent Bétermin, Peter Grabner, Stefan Steinerberger

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Mathematics of Computation
Volume	2022
DOIs	https://doi.org/10.1090/mcom/3706
Publication status	E-pub ahead of print - 17 May 2021

Keywords

math.NA
cs.NA
math.CA
65F15 (Primary), 31C20 (Secondary)

Access to Document

10.1090/mcom/3706

2105.07922v1Submitted manuscript, 129 KB

Cite this

@article{03a8eb7dc2674210a02b8c6622abdea1,

title = "How well-conditioned can the eigenvalue problem be?",

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. ",

keywords = "math.NA, cs.NA, math.CA, 65F15 (Primary), 31C20 (Secondary)",

author = "Carlos Beltr{\'a}n and Laurent B{\'e}termin and Peter Grabner and Stefan Steinerberger",

note = "6 pages, 2 figures",

year = "2021",

month = may,

day = "17",

doi = "10.1090/mcom/3706",

language = "English",

volume = "2022",

journal = "Mathematics of Computation",