A note on conjugate-gradient type methods for indefinite and/or inconsistent linear systems
type: Item
instance of: scholarly article
title: A note on conjugate-gradient type methods for indefinite and/or inconsistent linear systems
zbMATH Open document ID: 0847.65018
DOI: 10.1007/BF02142495
author: B. Fischer
author: Martin Hanke
author: Marlis Hochbruck
published in: Numerical Algorithms
publication date: 1996-04-28T00:00:00Z
review text: To design a conjugate gradient type method for a given linear system an inner product space has to be chosen and residual polynomials which minimize the induced norm have to be computed. In this paper a unified treatment of this approach for linear systems of equations with symmetric coefficient matrices is proposed. The authors mainly focus their attention on the application of such schemes to the solution of indefinite and/or inconsistent systems. Numerical examples are included.
reviewed by: Krassimir Georgiev
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 871281
zbMATH Keywords: indefinite systems
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: numerical examples
zbMATH Keywords: inconsistent systems
MaRDI profile type: Publication
cites work: On the solution of singular linear systems of algebraic equations by semiiterative methods
cites work: Q4886149
cites work: Q3313192
cites work: The method of minimum iterations with minimum errors for a system of linear algebraic equations with a symmetrical matrix
cites work: Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II
cites work: Q4843158
cites work: A Chebyshev-like semiiteration for inconsistent linear systems
cites work: Methods of conjugate gradients for solving linear systems
cites work: Solution of Sparse Indefinite Systems of Linear Equations
cites work: Q3262525
cites work: Q3965491
full work available at URL: https://doi.org/10.1007/bf02142495
OpenAlex ID: W2021415070
description: scientific article; zbMATH DE number 871281