Convergence rate estimates for iterative solutions of the biharmonic equation
type: Item
instance of: scholarly article
title: Convergence rate estimates for iterative solutions of the biharmonic equation
zbMATH Open document ID: 0675.65104
DOI: 10.1016/0377-0427(88)90348-2
author: Richard S. Varga
author: Garry Rodrigue
published in: Journal of Computational and Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The article is devoted to an analysis of the spectral radius of iteration matrices of finite-difference schemes approximating the biharmonic equation. The authors use the idea of \textit{P. R. Garabedian} [Math. Tables Aids Comput. 10, 183-185 (1956; Zbl 0073.108)] according to which the estimation of this radius in the form \(\rho =1-O(h^ k)\) can be reduced to the eigenvalue problem for some partial-differential operator. It is shown that the obtained estimates are precise for many classical iteration schemes. They can give also information on how much successful overrelaxation can improve the convergence rate. Some new iterative technics are suggested for which \(\rho =1-O(h)\).
reviewed by: Vladimir D. Korneev
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 31A30
zbMATH DE Number: 4106204
zbMATH Keywords: spectral radius
zbMATH Keywords: iteration matrices
zbMATH Keywords: finite-difference schemes
zbMATH Keywords: biharmonic equation
zbMATH Keywords: overrelaxation
zbMATH Keywords: convergence rate
MaRDI profile type: Publication
full work available at URL: 0377-0427(88)90348-2
OpenAlex ID: W2026532228
cites work: Estimation of the Relaxation Factor for Small Mesh Size
cites work: Q5342712
cites work: Q5639278
cites work: Q3909906
description: scientific article; zbMATH DE number 4106204