An overview of approaches for the stable computation of hybrid BiCG methods
type: Item
instance of: scholarly article
title: An overview of approaches for the stable computation of hybrid BiCG methods
zbMATH Open document ID: 0856.65022
DOI: 10.1016/0168-9274(95)00085-2
author: Gerard L. G. Sleijpen
author: Henk A. van der Vorst
published in: Applied Numerical Mathematics
publication date: 1997-02-24T00:00:00Z
review text: Some approaches that help to reduce the effects of local rounding errors in the BiCG iteration coefficients in hybrid schemes are presented. For example, a stabilization technique for the \(\text{BiCGstab}(l)\) method is proposed. Furthermore, look-ahead strategies for the determination of appropriate values for \(l\) in \(\text{BiCGstab}(l)\) are discussed. Some numerical examples show the advantages of the proposed methods.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 897511
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: nonsymmetric linear systems
zbMATH Keywords: hybrid methods
zbMATH Keywords: BiCG iteration
zbMATH Keywords: stabilization
zbMATH Keywords: look-ahead strategies
zbMATH Keywords: numerical examples
reviewed by: Michael Jung
describes a project that uses: CGS
describes a project that uses: BiCGstab
MaRDI profile type: Publication
full work available at URL: 0168-9274(95)00085-2
OpenAlex ID: W2127499737
cites work: An analysis of the composite step biconjugate gradient method
cites work: Treatment of near-breakdown in the CGS algorithm
cites work: A Theoretical Comparison of the Arnoldi and GMRES Algorithms
cites work: A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
cites work: A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems
cites work: Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
cites work: Q4091368
cites work: Generalized conjugate gradient squared
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: Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
cites work: Variants of BICGSTAB for Matrices with Complex Spectrum
cites work: Q4327529
cites work: A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
cites work: Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
cites work: Maintaining convergence properties of BiCGStab methods in finite precision arithmetic
cites work: Reliable updated residuals in hybrid Bi-CG methods
cites work: BiCGstab(\(l\)) and other hybrid Bi-CG methods
cites work: CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
cites work: The superlinear convergence behaviour of GMRES
description: scientific article; zbMATH DE number 897511