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

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Fachzeitschrift	Mathematics of Computation
Jahrgang	2022
DOIs	https://doi.org/10.1090/mcom/3706
Publikationsstatus	Elektronische Veröffentlichung vor Drucklegung. - 17 Mai 2021

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10.1090/mcom/3706

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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",