Performance comparison of preconditioned iterative methods with direct preconditioners
type: Item
instance of: scholarly article
zbMATH Open document ID: 1305.65119
author: Jae Heon Yun
author: Hyo Jin Lim
author: Kyoum Sun Kim
publication date: 2014-10-29T00:00:00Z
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F08
zbMATH DE Number: 6362185
zbMATH Keywords: preconditioned AOR method
zbMATH Keywords: \(L\)-matrix
zbMATH Keywords: irreducible matrix
zbMATH Keywords: triangular preconditioner
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: accelerated overrelaxation
zbMATH Keywords: preconditioning
MaRDI profile type: Publication
full work available at URL: jami.2014.389
OpenAlex ID: W2089071674
DOI: 10.14317/JAMI.2014.389
title: Performance comparison of preconditioned iterative methods with direct preconditioners
published in: Journal of Applied Mathematics \& Informatics
review text: Consider the matrix \(A=I-L-U\), a decomposition of the matrix \(A\) into a diagonal, a lower- and an upper triangular part. To solve \(Ax=b\), the preconditioners \(P\) of the form \(P_l=I+\beta L\), \(P_u=I+\beta U\), or \(P_b=I+\beta(L+U)\) can be applied. Then the original and the preconditioned system can be solved by an AOR (accelerated overrelaxation) iterative method. Comparison theorems are given for the (spectral radius of the) iteration matrices of the AOR methods with and without preconditioning. A near optimal selection of the parameter \(\beta\) for the Krylov method is proposed for each of the preconditioners.
reviewed by: Adhemar Bultheel
description: scientific article; zbMATH DE number 6362185