Convergence analysis of the preconditioned group splitting methods in boundary value problems
type: Item
instance of: scholarly article
title: Convergence analysis of the preconditioned group splitting methods in boundary value problems
zbMATH Open document ID: 1253.65039
DOI: 10.1155/2012/867598
author: Abdulkafi Mohammed Saeed
author: Norhashidah Hj. Mohd. Ali
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: The construction of a specific splitting-type preconditioner in block formulation applied to a class of group relaxation iterative methods derived from the centred and rotated (skewed) finite difference approximations has been shown to improve the convergence rates of these methods. In this paper, we present some theoretical convergence analysis on this preconditioner specifically applied to the linear systems resulted from these group iterative schemes in solving an elliptic boundary value problem. We will theoretically show the relationship between the spectral radiuses of the iteration matrices of the preconditioned methods which affects the rate of convergence of these methods. We will also show that the spectral radius of the preconditioned matrices is smaller than that of their unpreconditioned counterparts if the relaxation parameter is in a certain optimum range. Numerical experiments will also be presented to confirm the agreement between the theoretical and the experimental results.
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 6116463
zbMATH Keywords: splitting-type preconditioner in block formulation
zbMATH Keywords: finite difference approximations
Wikidata QID: Q58697002
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/867598
OpenAlex ID: W1989447454
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description: scientific article; zbMATH DE number 6116463