On the condition of the zeros of characteristic polynomials

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

1 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)72-84
Journal / PublicationJournal of Complexity
Volume42
Online published7 Apr 2017
Publication statusPublished - Oct 2017

Abstract

We prove that the expectation of the logarithm of the condition number of each of the zeros of the characteristic polynomial of a complex standard Gaussian matrix is
Ω (n) (the real and imaginary parts of the entries of a Gaussian matrix are independent standard Gaussian random variables). This may provide a theoretical explanation for the common practice in numerical linear algebra that advises against computing eigenvalues via root-finding for characteristic polynomials.

Research Area(s)

  • Characteristic polynomial, Condition, Eigenvalues, Random matrices

Citation Format(s)

On the condition of the zeros of characteristic polynomials. / Bürgisser, Peter; Cucker, Felipe; Rocha Cardozo, Elisa.

In: Journal of Complexity, Vol. 42, 10.2017, p. 72-84.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review