A Krylov multisplitting algorithm for solving linear systems of equations
type: Item
instance of: scholarly article
title: A Krylov multisplitting algorithm for solving linear systems of equations
zbMATH Open document ID: 0792.65019
DOI: 10.1016/0024-3795(93)90110-A
author: Chiou-Ming Huang
author: Dianne P. O'Leary
published in: Linear Algebra and its Applications
publication date: 1994-03-27T00:00:00Z
review text: The Krylov subspace methods (conjugate gradients, GMRES, etc.) for parallel computers are analysed in cases where the preconditioning matrix arises from multisplitting. The algorithm is effectively divided into tasks that generate search directions and a single task minimizing over the resulting subspaces. The convergence properties of various forms of the algorithm are examined, and numerical examples are given.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 540054
zbMATH Keywords: conjugate gradients
zbMATH Keywords: Krylov subspace methods
zbMATH Keywords: GMRES
zbMATH Keywords: parallel computers
zbMATH Keywords: preconditioning
zbMATH Keywords: multisplitting
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
reviewed by: F. Szidarovszky
MaRDI profile type: Publication
cites work: A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable-Step Preconditioning
cites work: Q4001523
cites work: Rang revealing QR factorizations
cites work: On the efficient implementation of preconditioned s-step conjugate gradient methods on multiprocessors with memory hierarchy
cites work: \(H\)-splittings and two-stage iterative methods
cites work: Q3935372
cites work: Q5185900
cites work: Convergence of parallel multisplitting iterative methods for M-matrices
cites work: Ordering Schemes for Parallel Processing of Certain Mesh Problems
cites work: Parallel QR factorization by Householder and modified Gram-Schmidt algorithms
cites work: Multi-Splittings of Matrices and Parallel Solution of Linear Systems
cites work: Efficient Implementations of Certain Iterative Methods
cites work: Parallel algorithms and architectures for multisplitting iterative methods
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: Multisplitting with Different Weighting Schemes
full work available at URL: 0024-3795(93)90110-a
OpenAlex ID: W2069332482
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description: scientific article; zbMATH DE number 540054