Random-walk interpretations of classical iteration methods
type: Item
instance of: scholarly article
title: Random-walk interpretations of classical iteration methods
zbMATH Open document ID: 0821.65014
DOI: 10.1016/0024-3795(93)00101-5
author: Neal Madras
author: Jonathan Goodman
published in: Linear Algebra and its Applications
publication date: 1995-06-12T00:00:00Z
review text: Simple probabilistic interpretations of classical Jacobi and Gauss-Seidel iteration methods for discrete Laplacian operators are given. The probability background is illustrated on three examples. The random-walk interpretation is discussed to compare convergence rates of different relaxation methods (Gauss-Seidel standard ordering, Gauss-Seidel red- black ordering, \(2 \times 2\) block Jacobi, \(2 \times 2\) block Gauss- Seidel standard ordering) for the five-point Laplacian. The procedure is extended for the nine-point Laplacian. The underrelaxation technique is discussed.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 753881
zbMATH Keywords: random-walk interpretations
zbMATH Keywords: Jacobi method
zbMATH Keywords: Gauss-Seidel standard ordering
zbMATH Keywords: probabilistic interpretations
zbMATH Keywords: Gauss-Seidel iteration methods
zbMATH Keywords: discrete Laplacian operators
zbMATH Keywords: convergence rates
zbMATH Keywords: relaxation methods
zbMATH Keywords: Gauss-Seidel red-black ordering
zbMATH Keywords: five-point Laplacian
zbMATH Keywords: nine-point Laplacian
zbMATH Keywords: underrelaxation
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)00101-5
OpenAlex ID: W1982863946
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description: scientific article; zbMATH DE number 753881