A comparison of iterative methods to solve complex valued linear algebraic systems
type: Item
instance of: scholarly article
title: A comparison of iterative methods to solve complex valued linear algebraic systems
zbMATH Open document ID: 1307.65034
author: Owe Axelsson
author: Bashir Ahmad
author: M. Neytcheva
published in: Numerical Algorithms
publication date: 2014-08-29T00:00:00Z
review text: This overview and analysis of various iterative methods to solve sparse complex linear equations includes both preconditioning and splitting methods as well as extensive and detailed tests and numerical experiments. In general, it is advisable to replace a sparse complex linear system \(Cz = h \in \mathbb C^n\) by a \(2n\) by \(2n\) real system such as \( \begin{bmatrix} A & -B\\B & A \end{bmatrix} \begin{pmatrix} x\\y \end{pmatrix} = \begin{pmatrix} f\\g \end{pmatrix}\) or \( \begin{bmatrix} B & -A\\A & B \end{bmatrix} \begin{pmatrix} x\\-y \end{pmatrix} = \begin{pmatrix} g\\f \end{pmatrix}\) where \(C = A + iB, \;z = x+iy\) and \(h = f+ig\) and all right hand entries in the last three equations are real, except for \(i = \sqrt{-1}\). The advice in the conclusions section should be heeded by anyone in need solving complex sparse linear systems.
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65E05
zbMATH DE Number: 6335812
zbMATH Keywords: complex linear equation
zbMATH Keywords: complex symmetric system
zbMATH Keywords: preconditioning
zbMATH Keywords: splitting method
zbMATH Keywords: numerical test
zbMATH Keywords: sparse matrix
describes a project that uses: SparseMatrix
describes a project that uses: AGMG
MaRDI profile type: Publication
full work available at URL: s11075-013-9764-1
OpenAlex ID: W2089393890
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DOI: 10.1007/S11075-013-9764-1
description: scientific article; zbMATH DE number 6335812