Projected iterative algorithms for complex symmetric systems arising in magnetized multicomponent transport
type: Item
instance of: scholarly article
title: Projected iterative algorithms for complex symmetric systems arising in magnetized multicomponent transport
zbMATH Open document ID: 1161.65025
author: Vincent Giovangigli
author: Benjamin Graille
published in: Linear Algebra and its Applications
publication date: 2009-02-10T00:00:00Z
review text: The problem is to solve a constrained linear system \({\mathcal G}a=b\), \(a\in{\mathcal C}\) with \({\mathcal G}=G+iG'\) a \(n\times n\) complex matrix, symmetric (not hermitian!) with \(G\) positive semi-definite, and a nullspace \(N(G)\) satisfying \(G'N(G)=0\). The linear space \({\mathcal C}=C+iC\) is a complexification of \(C\) with \(C\oplus N(G)={\mathbb R}^n\). The problem has been studied before in the case \(G'=0\) [cf. \textit{A. Ern} and \textit{V. Giovangigli}, Linear Algebra Appl. 250, 289--315 (1997; Zbl 0867.65017)]. The natural solution of the problem involves a generalized inverse with prescribed range and nullspace. First it is shown that this generalized inverse can be chosen to be symmetric. The symmetry and positive definiteness allows to use a complex Cholesky factorization method. Next it is shown that the convergence of a projected stationary iterative method for an appropriate splitting of the matrix \({\mathcal G}\) is similar to the case \(G'=0\). On the other hand, the (preconditioned) orthogonal projected residual method, makes use of the symmetry and positivity properties of the real part, whence it has better convergence properties in general. Applications in magnetized multicomponent transport are included.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 5505637
zbMATH Keywords: constrained linear system
zbMATH Keywords: symmetric generalized inverse
zbMATH Keywords: iterative method
zbMATH Keywords: multicomponent transport
zbMATH Keywords: preconditioning
zbMATH Keywords: complex Cholesky factorization method
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.laa.2008.11.001
OpenAlex ID: W2051625925
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DOI: 10.1016/J.LAA.2008.11.001
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description: scientific article; zbMATH DE number 5505637