Asynchronous block-iterative methods for almost linear equations
type: Item
instance of: scholarly article
title: Asynchronous block-iterative methods for almost linear equations
zbMATH Open document ID: 0729.65033
DOI: 10.1016/0024-3795(91)90391-9
author: Amit Bhaya
author: Francisco Mota
author: Eugenius Kaszkurewicz
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: On a distributed multiprocessor with asynchronous communication, a block relaxation method is considered for the solution of a large system of equations with linear and Lipschitz-continuous nonlinear part. For bounded communication delays the authors show how to transform the iteration into standard form; then a general sufficient convergence condition is formulated. The method has been implemented on a 4-processor transputer with direct connections between all processors. On a 44\(\times 44\) system (not shown but said to be from power network background), convergence times of synchronous and asynchronous iterations are compared and speedups reported (of about 2); \(\omega =1\) was observed to be optimal. The choice of the partition of the matrix is said to be crucial but difficult.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y10
zbMATH DE Number: 4205877
zbMATH Keywords: block-iterative methods
zbMATH Keywords: almost linear equations
zbMATH Keywords: distributed multiprocessor
zbMATH Keywords: block relaxation method
zbMATH Keywords: convergence
zbMATH Keywords: asynchronous iterations
zbMATH Keywords: speedups
MaRDI profile type: Publication
full work available at URL: 0024-3795(91)90391-9
OpenAlex ID: W1995346450
cites work: Asynchronous Iterative Methods for Multiprocessors
cites work: Q4001523
cites work: Chaotic relaxation
cites work: Some convergence results for asynchronous algorithms
cites work: Q3359644
cites work: On stability of discrete composite systems
cites work: On the convergence of parallel asynchronous block-iterative computations
cites work: Q4074310
cites work: Asynchronous Relaxations for the Numerical Solution of Differential Equations by Parallel Processors
cites work: Q3993065
cites work: Q5652137
cites work: Contraction en norme vectorielle: Convergence d'itérations chaotiques pour des équations non linéaires de point fixe à plusieurs variables
cites work: Nested Epsilon Decompositions of Linear Systems: Weakly Coupled and Overlapping Blocks
cites work: Q5342712
cites work: Parallel Algorithms for Nonlinear Problems
cites work: Q5604166
Wikidata QID: Q127065873
description: scientific article; zbMATH DE number 4205877