A QR algorithm with variable iteration multiplicity
type: Item
instance of: scholarly article
title: A QR algorithm with variable iteration multiplicity
zbMATH Open document ID: 0895.65011
DOI: 10.1016/S0377-0427(97)00151-9
author: A. A. Dubrulle
published in: Journal of Computational and Applied Mathematics
publication date: 1998-09-02T00:00:00Z
review text: Each step of an implicit multishift QR algorithm consists of first applying an \(m\times m\) orthogonal transformation, determined by the shifts, which causes a bulge of size \(m\) on the Hessenberg matrix, and then to eliminate that bulge with a sequence of orthogonal transformations. This process may suffer from forward instability and it is discussed how the multiplicity \(m\) should be chosen and the implementation done, to avoid ill effects of this forward instability.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1115928
zbMATH Keywords: variable iteration multiplicity
zbMATH Keywords: implicit multishift QR algorithm
zbMATH Keywords: Hessenberg matrix
zbMATH Keywords: orthogonal transformations
zbMATH Keywords: forward instability
reviewed by: Axel Ruhe
describes a project that uses: LAPACK
describes a project that uses: EISPACK
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1115928