A linear system solver based on a modified Krylov subspace method for breakdown recovery
type: Item
instance of: scholarly article
title: A linear system solver based on a modified Krylov subspace method for breakdown recovery
zbMATH Open document ID: 0858.65034
DOI: 10.1007/BF02141750
author: Charles Tong
author: Qiang Ye
published in: Numerical Algorithms
publication date: 1996-08-11T00:00:00Z
review text: The authors present a scheme based on a modified Krylov subspace approach to Lanczos' biorthogonalization method of the solution of nonsymmetric linear systems. When the scheme breaks down it is replaced by a modified dual Krylov subspace which is the sum of the original subspace and a new Krylov subspace which depends on a new start vector and the original matrix. Based on this strategy, they develop a practical algorithm for solving linear systems (the MLAN/QM algorithm) which also incorporates the residual quasi-minimization proposed by \textit{R. W. Freund} and \textit{N. M. Nachtigal} [Numer. Math. 60, No. 3, 315-339 (1991; Zbl 0754.65034)]. The algorithm is presented in some computational detail. Convergence bounds for the method are presented as well as numerical results to show its effectiveness.
reviewed by: D. Kershaw
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 915392
zbMATH Keywords: Krylov subspace method
zbMATH Keywords: breakdown recovery
zbMATH Keywords: convergence
zbMATH Keywords: Lanczos' biorthogonalization method
zbMATH Keywords: nonsymmetric linear systems
zbMATH Keywords: MLAN/QM algorithm
zbMATH Keywords: residual quasi-minimization
zbMATH Keywords: algorithm
zbMATH Keywords: numerical results
describes a project that uses: na1
describes a project that uses: Harwell-Boeing sparse matrix collection
MaRDI profile type: Publication
cites work: Nonsymmetric Lanczos and finding orthogonal polynomials associated with indefinite weights
cites work: Avoiding breakdown in the CGS algorithm
cites work: Lanczos-type algorithms for solving systems of linear equations
cites work: Avoiding breakdown and near-breakdown in Lanczos type algorithms
cites work: Sparse matrix test problems
cites work: Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
cites work: Q4091368
cites work: An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
cites work: QMR: A quasi-minimal residual method for non-Hermitian linear systems
cites work: Q3359644
cites work: Matrix interpretations and applications of the continued fraction algorithm
cites work: A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
cites work: A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II
cites work: Low-Rank Modification of the Unsymmetric Lanczos Algorithm
cites work: Lanczos Methods for the Solution of Nonsymmetric Systems of Linear Equations
cites work: Reduction to Tridiagonal Form and Minimal Realizations
cites work: A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms
description: scientific article; zbMATH DE number 915392