Parallel methods for tridiagonal equations
type: Item
instance of: scholarly article
title: Parallel methods for tridiagonal equations
zbMATH Open document ID: 0651.65027
DOI: 10.1007/BF02251254
author: S. H. Smith
published in: Computing
publication date: 1988-01-01T00:00:00Z
review text: The authors present parallel adaptations of the Gauss-Seidel iterative method for solving tridiagonal systems of linear algebraic equations. Two of them possess a similarity to the marching principle developed previously for solving block-tridiagonal systems arising in the numerical solution of partial differential equations while the third one is based on the red-black ordering of the unknowns. The computational work is distributed proportionally among slave processors of the parallel system considered, yielding almost optimal speed-up values. The methods are compared from a point of view of the number of arithmetic and communication operations required. Through the parallelization a convergence property of the original methods is preserved. The experience achieved by the simulation can be applied also to other parallel MIMD-type computer configurations.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 4062470
zbMATH Keywords: parallel methods
zbMATH Keywords: Gauss-Seidel iterative method
zbMATH Keywords: tridiagonal systems
zbMATH Keywords: red-black ordering
zbMATH Keywords: convergence
reviewed by: Marián Vajteršic
MaRDI profile type: Publication
cites work: Alternating sequential/parallel processing
cites work: Alternating sequential-parallel calculation of eigenvalues for symmetric matrices
full work available at URL: https://doi.org/10.1007/bf02251254
OpenAlex ID: W101662044
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description: scientific article; zbMATH DE number 4062470