On a conjugate gradient-type method for solving complex symmetric linear systems
type: Item
instance of: scholarly article
title: On a conjugate gradient-type method for solving complex symmetric linear systems
zbMATH Open document ID: 0941.65031
DOI: 10.1016/S0024-3795(98)10091-5
author: Angelika Bunse-Gerstner
author: Ronald Stöver
published in: Linear Algebra and its Applications
publication date: 2000-07-20T00:00:00Z
review text: The authors present a new conjugate gradient-type iterative method (CSYM) for solving large sparse systems of linear equations with complex coefficient matrices. The method is based on unitary equivalence transformations of the coefficient matrix to complex symmetric tridiagonal form. The procedure used in the algorithm is similar to the procedure applied in the well known Lanczos method. One can find an excellent description of the new technique with theoretical part, comparison with two often used algorithms (CGNR and QMR) by some theoretical investigations as well as by numerical examples which are well chosen and representative. The new algorithm is analyzed and some theoretical statements are given. It is shown that it is fundamentally different from Krylov subspace methods when the original complex symmetric problem is reformulated as a real problem of twice the dimension. The numerical results which are shown in the figures of the paper give a good impression about the performance of all three methods even if they are used without preconditioning.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65E05
zbMATH DE Number: 1331748
zbMATH Keywords: complex coefficient matrices
zbMATH Keywords: conjugate gradient-type iterative method
zbMATH Keywords: normal equations
zbMATH Keywords: sparse matrices
zbMATH Keywords: large sparse systems of linear equations
zbMATH Keywords: algorithm
zbMATH Keywords: Lanczos method
zbMATH Keywords: numerical examples
zbMATH Keywords: Krylov subspace methods
reviewed by: Krassimir Georgiev
describes a project that uses: Harwell-Boeing sparse matrix collection
MaRDI profile type: Publication
cites work: Singular value decompositions of complex symmetric matrices
cites work: Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
cites work: Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices
cites work: Matrix Analysis
cites work: A fast minimal residual algorithm for shifted unitary matrices
cites work: How Fast are Nonsymmetric Matrix Iterations?
cites work: Two Conjugate-Gradient-Type Methods for Unsymmetric Linear Equations
Wikidata QID: Q127908571
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description: scientific article; zbMATH DE number 1331748