Two-way bidiagonalization scheme for downdating the singular-value decomposition
type: Item
instance of: scholarly article
title: Two-way bidiagonalization scheme for downdating the singular-value decomposition
zbMATH Open document ID: 0833.65033
DOI: 10.1016/0024-3795(93)00273-3
author: Haesun Park
author: Sabine Van Huffel
published in: Linear Algebra and its Applications
publication date: 1996-03-24T00:00:00Z
review text: Downdating of a matrix means the deletion of an existing row of this matrix. It is shown that the problem of downdating a row in the singular value decomposition of a matrix can be transformed into a problem of bidiagonalizing a diagonal matrix bordered by a column and then diagonalizing this bidiagonal matrix. For the bidiagonalization of a rank-\(r\) matrix a two-way chasing scheme is proposed. Using this method the computation time is reduced by nearly 50\% for large \(r\) compared to one-way chasing schemes.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 778233
zbMATH Keywords: bidiagonal matrix
zbMATH Keywords: parallel computation
zbMATH Keywords: downdating
zbMATH Keywords: singular value decomposition
zbMATH Keywords: diagonalizing
reviewed by: René Lamour
describes a project that uses: VanHuffel
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)00273-3
OpenAlex ID: W2029765191
cites work: Accurate Downdating of Least Squares Solutions
cites work: Updating the singular value decomposition
cites work: Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
cites work: Q3359644
cites work: Q4072724
cites work: Implementation of adaptive array algorithms
cites work: The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization
cites work: Parallel tri- and bi-diagonalization of bordered bidiagonal matrices
cites work: Q4001897
description: scientific article; zbMATH DE number 778233