Abstract

In this paper we revisit the problem of performing a QR-step on an unreducedHessenberg matrix H when we know an "exact" eigenvalue ?0 of H. Under exact arithmetic, thiseigenvalue will appear on diagonal of the transformed Hessenberg matrix H~ and will be decoupledfrom the remaining part of the Hessenberg matrix, thus resulting in a deflation. But it is well knownthat in finite precision arithmetic the so-called perfect shift can get blurred and that the eigenvalue ?0can then not be deflated and/or is perturbed significantly. In this paper, we develop a new strategyfor computing such a QR step so that the deflation is almost always successful. We also show howto extend this technique to double QR-steps with complex conjugate shifts.

Autore Pugliese

• Mastronardi Nicola

Tutti gli autori

• N. Mastronardi; P. Van Dooren

Titolo volume/Rivista

SIAM journal on matrix analysis and applications

Anno di pubblicazione

2018

ISSN

0895-4798

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

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Numero di citazioni Scopus

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Ultimo Aggiornamento Citazioni

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Settori ERC

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Codici ASJC

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