On the \(LU\) factorization of infinite systems of semi-separable equations
type: Item
instance of: scholarly article
title: On the \(LU\) factorization of infinite systems of semi-separable equations
zbMATH Open document ID: 1272.65030
author: Patrick M. Dewilde
published in: Indagationes Mathematicae. New Series
publication date: 2012-12-06T00:00:00Z
review text: Closed and canonical expressions for the \(LU\) factors and related existence theorems and factorization algorithms for the case where the original system is invertible and the factors are required to have inverses as the same type as themselves. The author focuses on \(LU\) factorization in the context of infinitely indexed systems. The main tool used is canonical forms. The resulting algorithm is independent of the existence of the solution and has, in addition, the very nice property that it only uses orthogonal transformations. It is shown that the computation of subsequent partial Schur complements is numerically stable.
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 6112941
zbMATH Keywords: infinite systems
zbMATH Keywords: \(LU\)-factorization
zbMATH Keywords: \(QR\)-factorization
zbMATH Keywords: semi-separable systems
zbMATH Keywords: inner-outer factorization
zbMATH Keywords: canonical forms
zbMATH Keywords: pivots
zbMATH Keywords: spectral factorization
zbMATH Keywords: square-root equation
zbMATH Keywords: algorithm
zbMATH Keywords: Schur complement
reviewed by: R. P. Tewarson
MaRDI profile type: Publication
full work available at URL: j.indag.2012.09.004
OpenAlex ID: W2026535708
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DOI: 10.1016/J.INDAG.2012.09.004
description: scientific article; zbMATH DE number 6112941