On Hamiltonian and symplectic Lanczos processes
type: Item
instance of: scholarly article
title: On Hamiltonian and symplectic Lanczos processes
zbMATH Open document ID: 1062.65047
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: The author examines the relationship between various structure-preserving Krylov subspace methods for computing partial eigensystems of large sparse skew-Hamiltonian, Hamiltonian and symplectic matrices. Parameters in families of implicitly restarted Lanczos methods, proposed by \textit{P. Benner} and \textit{H. Fassbender} [ibid. 263, 75--111 (1987; Zbl 0884.65028); SIAM J. Matrix Anal. Appl. 22, No.~3, 682--713 (2000; Zbl 0985.65026)], are selected to condense the process as much as possible. The condensed Hamiltonian Lanczos process applied to the Hamiltonian matrix \(H\) is shown to be equivalent to the unsymmetric Lanczos process applied to the skew-Hamiltonian matrix \(H^2\) but to require roughly half as much computation. The condensed symplectic Lanczos process applied to a symplectic matrix \(S\) is shown to be equivalent to the unsymmetric Lanczos process applied to \(S+S^{-1}\) and to require roughly half as much computation.
reviewed by: Alan L. Andrew
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 2083505
zbMATH Keywords: eigenvalues
zbMATH Keywords: Lanczos process
zbMATH Keywords: Hamiltonian matrices
zbMATH Keywords: symplectic matrices
zbMATH Keywords: implicit restarts
zbMATH Keywords: Krylov subspace methods
author: David S. Watkins
describes a project that uses: ARPACK
describes a project that uses: IRAM
describes a project that uses: eigs
MaRDI profile type: Publication
full work available at URL: j.laa.2002.11.001
OpenAlex ID: W2055260148
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DOI: 10.1016/J.LAA.2002.11.001
description: scientific article; zbMATH DE number 2083505