A generalized isometric Arnoldi algorithm
type: Item
instance of: scholarly article
title: A generalized isometric Arnoldi algorithm
zbMATH Open document ID: 1123.65047
author: Michael Stewart
published in: Linear Algebra and its Applications
publication date: 2007-05-10T00:00:00Z
review text: Suppose \(A\) is an isometry on a Hilbert space. The author shows that the isometric Arnoldi algorithm yields a sequence of matrices \(M_{j}\) and can be interpreted as a structured form of a modified Gram-Schmidt process. The algorithm is described in terms of projections and inner products. Numerical experiments suggest that compared to a generalized Schur algorithm, the new one improves the numerical orthogonality of the sequence. Contents: Introduction; A general form of the isometric Arnoldi algorithm; Krylov-like sequences; Orthogonality relations; The factored algorithm; Computing QR factorization; Preliminary numerical experiments; Additional topics.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65F25
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 5151561
zbMATH Keywords: orthogonalization
zbMATH Keywords: fast algorithms
zbMATH Keywords: Schur algorithm
zbMATH Keywords: isometric Arnoldi algorithm
zbMATH Keywords: structured matrices
zbMATH Keywords: Hilbert space
zbMATH Keywords: Gram-Schmidt process
zbMATH Keywords: numerical experiments
zbMATH Keywords: Krylov-like sequences
zbMATH Keywords: QR factorization
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: j.laa.2006.12.021
OpenAlex ID: W1974631534
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DOI: 10.1016/J.LAA.2006.12.021
description: scientific article; zbMATH DE number 5151561