Perturbation analysis for block downdating of a Cholesky decomposition
type: Item
instance of: scholarly article
title: Perturbation analysis for block downdating of a Cholesky decomposition
zbMATH Open document ID: 0808.65042
author: Lars Eldén
author: Haesun Park
published in: Numerische Mathematik
publication date: 1994-11-21T00:00:00Z
review text: Let the Cholesky decomposition of \(X^ T X\) be \(X^ T X = R^ T R\), where \(R\) is upper triangular. The Cholesky block downdating problem is to determine \(\widetilde{R}\) such that \(\widetilde{R}^ T \widetilde{R} = R^ T R - Z^ T Z\), where \(Z\) is a block of rows from the data matrix \(X\). This paper analyzes the sensitivity of this block downdating problem of the Cholesky factorization. A measure of conditioning for the Cholesky block downdating is presented and compared to the single row downdating case.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 691552
zbMATH Keywords: Cholesky decomposition
zbMATH Keywords: block downdating problem
zbMATH Keywords: sensitivity
zbMATH Keywords: Cholesky factorization
zbMATH Keywords: conditioning
reviewed by: I. N. Katz
MaRDI profile type: Publication
full work available at URL: s002110050072
OpenAlex ID: W2076948696
DOI: 10.1007/S002110050072
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description: scientific article; zbMATH DE number 691552