On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems
type: Item
instance of: scholarly article
title: On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems
zbMATH Open document ID: 0848.65026
DOI: 10.1007/BF01739820
author: Mårten Gulliksson
published in: BIT
publication date: 1996-10-27T00:00:00Z
review text: It is shown how the modified Gram-Schmidt algorithm can be used for constrained and weighted linear least squares problems. The equivalence between the weighted modified Gram-Schmidt algorithm and an algorithm based on a weighted Householder-like QR factorization applied to a slightly larger problem is used to explain the instability of the proposed algorithm. Also, it is shown how the orthogonality of the calculated \(Q\) from the weighted modified Gram-Schmidt can be improved by performing reorthogonalization. Finally, numerical results are given to illustrate the main features of the algorithm.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F25
zbMATH DE Number: 844662
zbMATH Keywords: Gram-Schmidt algorithm
zbMATH Keywords: weighted linear least squares problems
zbMATH Keywords: factorization
zbMATH Keywords: instability
zbMATH Keywords: reorthogonalization
zbMATH Keywords: numerical results
reviewed by: Florica Luban
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01739820
OpenAlex ID: W2073148407
description: scientific article; zbMATH DE number 844662