Convergence of a direct-iterative method for large-scale least-squares problems
type: Item
instance of: scholarly article
title: Convergence of a direct-iterative method for large-scale least-squares problems
zbMATH Open document ID: 0576.65026
DOI: 10.1016/0024-3795(85)90073-4
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: Es gibt lineare Ausgleichsprobleme (1) \(Ax=b\) (z.B. in der Geodäsie), bei denen sich die \(m\times n\)-Matrix A so in Blöcke \(A^ T=(A1,A2)^ T\) zerlegen läßt, daß die \(n\times n\)-Matrix A1 nichtsingulär ist und für A1 relative leicht eine Faktorisierung angegeben werden kann. Die eindeutige Lösung des Ausgleichsproblems ist ein Teil der Lösung eines linearen Gleichungssystems (2) \(Cy=d\) mit regulärer \((m+n)\times (m+n)\)-Matrix C. In der vorliegenden Arbeit wird das Block- SOR-Verfahren auf (2) angewandt. Die Blockeinteilung von C wird so gewählt, daß eine schwach zweizyklische Jacobimatrix J entsteht [vgl. \textit{R. S. Varga}, Matrix iterative analysis (1963; Zbl 0133.086)]; das Verfahren erfordert dann in jedem Schritt die Lösung eines linearen Systems mit der Matrix A1. Benutzt man nun, daß \(J^ 2\) nur nichtpositive Eigenwerte besitzt, so läßt sich der optimale (Unter- )Relaxationsparameter und das Konvergenzintervall für den Parameter angeben.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 3921821
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: least-squares problems
zbMATH Keywords: optimum SOR
zbMATH Keywords: parameter
zbMATH Keywords: combined direct-iterative method
zbMATH Keywords: asymptotic
zbMATH Keywords: convergence factor
zbMATH Keywords: 2-cyclic block SOR method
author: Thomas L. Markham
author: M. Neumann
author: Robert J. Plemmons
describes a project that uses: symrcm
describes a project that uses: MA28
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90073-4
OpenAlex ID: W2022838819
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description: scientific article; zbMATH DE number 3921821