Accelerating with rank-one updates
type: Item
instance of: scholarly article
title: Accelerating with rank-one updates
zbMATH Open document ID: 0683.65018
DOI: 10.1016/0024-3795(89)90719-2
author: Olavi Nevanlinna
author: Timo Eirola
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: One considers the iteration \(x_{k+1}=x_ k+H_ k(b-Ax_ k)\) for solving systems of linear algebraic equations \(Ax=b\) with a square non- singular matrix A. Special emphasis is put on the choice of the matrix \(H_ k\). One improves \(H_ k\) during each step in such a way that with increasing number of iterations the sequence of matrices \(H_ k\) tends to \(A^{-1}\). This is obtained by using the rank-one updates \(H_ k\) on each step of modification. Sufficient conditions are derived under which the matrices \(H_ k\) are not singular for any \(x_ 0\) and \(H_ 0\). Necessary and sufficient conditions are obtained under which the matrix \(H_ k+I\) becomes singular under the assumption that the matrix \(H_ k\) is not singular. One presents an algorithm which realizes the iterative process.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4119486
zbMATH Keywords: convergence acceleration
zbMATH Keywords: rank-one updates
zbMATH Keywords: iterative process
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90719-2
OpenAlex ID: W1963604564
cites work: Q4091368
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: Q3698204
cites work: Q5674306
Recommended article: Q5479896
Recommended article: A new approach to symmetric rank-one updating
Recommended article: A Theoretical and Experimental Study of the Symmetric Rank-One Update
Recommended article: Q4483859
Recommended article: Q5184684
Recommended article: Metric-based symmetric rank-one updates
Recommended article: Fast matrix rank algorithms and applications
description: scientific article; zbMATH DE number 4119486