Accurate downdating of a modified Gram-Schmidt QR decomposition
type: Item
instance of: scholarly article
title: Accurate downdating of a modified Gram-Schmidt QR decomposition
zbMATH Open document ID: 0848.65014
DOI: 10.1007/BF01740553
author: Haesun Park
author: Kyeongah Yoo
published in: BIT
publication date: 1996-11-03T00:00:00Z
review text: Given \({z^T \choose \widetilde X} = X\), \(\widetilde{X} = \widetilde{Q} {R\choose 0}\). Find \(R\), such that \(X = Q {R \choose 0}\). A new algorithm for this process (which the authors call downdating) is presented. The relationship of the process to full Householder QR decomposition is explored and then used to derive an algorithm that improves the Gram-Schmidt downdating algorithm. Results of numerical tests are given. These results show that the proposed algorithm produces more accurate results than the usual algorithm for certain ill-conditioned problems.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 881192
zbMATH Keywords: algorithm
zbMATH Keywords: downdating
zbMATH Keywords: Householder QR decomposition
zbMATH Keywords: Gram-Schmidt down-dating algorithm
zbMATH Keywords: numerical tests
zbMATH Keywords: ill-conditioned problems
reviewed by: R. P. Tewarson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 881192