Matrix algorithms. Vol. 2: Eigensystems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0984.65031
DOI: 10.1137/1.9780898718058
author: G. W. Stewart
publication date: 2001-11-06T00:00:00Z
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65-01
Mathematics Subject Classification ID: 00A06
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1669150
zbMATH Keywords: Arnoldi method
zbMATH Keywords: eigenvalues
zbMATH Keywords: singular values
zbMATH Keywords: Krylov methods
zbMATH Keywords: subspace iteration
zbMATH Keywords: Jacobi-Davidson iteration
zbMATH Keywords: Lanczos method
zbMATH Keywords: matrix algorithm
zbMATH Keywords: QR algorithm
zbMATH Keywords: numerical linear algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1137/1.9780898718058
OpenAlex ID: W4242722506
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title: Matrix algorithms. Vol. 2: Eigensystems
review text: This second volume in a series of 5 on matrix algorithms is devoted to eigenvalue-eigenvector computations. As in the first volume on basic decompositions (1998; Zbl 0910.65012), the approach is very constructive, algorithmic, and self contained. The author has chosen not to heavily cross reference between the different volumes but to assume a general understanding of what is needed from the previous theory and algorithms. The first part concentrates on general dense matrices and the main issues are subsequently: the general theory, the QR algorithm, and the symmetric eigenvalue problem. Also singular values and the generalized eigenvalue problem are discussed here. In the second part large matrices are treated. Again the general theory is given and is followed by Krylov methods (in particular Arnoldi and Lanczos). The last chapter shifts to subspace iteration and the Jacobi-Davidson method. NEWLINENEWLINENEWLINEThe material for this second volume is less elementary than in the first volume. Yet the author succeeds again in picking up the essential stepping stones to allow the student or the practinoner, who might not be a specialist in numerical linear algebra, to safely embark the reading of this volume. It confirms the expectation that the whole series will grow out to be a reference work for the next generation.
reviewed by: Adhemar Bultheel
description: scientific article; zbMATH DE number 1669150