Iterative algorithms for Gram-Schmidt orthogonalization
type: Item
instance of: scholarly article
title: Iterative algorithms for Gram-Schmidt orthogonalization
zbMATH Open document ID: 0667.65037
DOI: 10.1007/BF02241222
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: A Gram-Schmidt algorithm to orthogonalize a sequence of vectors, where one vector at a time is orthogonalized to the set of already orthogonalized vectors is investigated. It is shown that if a reorthogonalization is performed whenever the norm of the vector is decreased more than a certain threshold, a prescribed accuracy of the whole sequence will be obtained both for the classical and the modified variants of the Gram-Schmidt algorithm.
Mathematics Subject Classification ID: 65F25
Mathematics Subject Classification ID: 65G50
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 4092662
zbMATH Keywords: Gram-Schmidt orthogonalization
zbMATH Keywords: QR factorization
zbMATH Keywords: vector algorithms
zbMATH Keywords: Gram-Schmidt algorithm
author: Walter Hoffmann
reviewed by: Axel Ruhe
MaRDI profile type: Publication
cites work: Solving linear least squares problems by Gram-Schmidt orthogonalization
cites work: Handbook series linear algebra. Linear least squares solutions by Householder transformations
cites work: Rang revealing QR factorizations
cites work: Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
cites work: Q5185900
cites work: Q3868672
cites work: Numerical aspects of Gram-Schmidt orthogonalization of vectors
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description: scientific article; zbMATH DE number 4092662