A note on simultaneous preconditioning and symmetrization of non-symmetric linear systems.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1245.65033
author: Nassif Ghoussoub
author: Amir Moradifam
published in: Numerical Linear Algebra with Applications
publication date: 2012-06-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/0801.3865
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 6043443
zbMATH Keywords: iterative method
zbMATH Keywords: sparse matrix
zbMATH Keywords: Lanczos method
zbMATH Keywords: conjugate gradients
zbMATH Keywords: preconditioning
zbMATH Keywords: MINRES
zbMATH Keywords: SYMMLQ
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
OpenAlex ID: W2105813930
arXiv ID: 0801.3865
cites work: A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part
cites work: Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
cites work: Q3410058
cites work: Q4551558
cites work: Q4348514
cites work: Q4414854
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations
cites work: Q3609572
cites work: Anti-self-dual Lagrangians: variational resolutions of non-self-adjoint equations and dissipative evolutions
DOI: 10.1002/NLA.730
title: A note on simultaneous preconditioning and symmetrization of non-symmetric linear systems.
review text: The paper describes a technique for simultaneous preconditioning and symmetrization for solving large, sparse and non-symmetric problems by CG, MINRES or SYMMLQ. The approach is based on the theory of self-duality. The paper states that sometimes it is beneficial to replace the original problem \(Ax = b\) with non-symmetric matrix \(A\) by \(A^TMAx = A^TMb\). It is shown how to choose the matrix \(M\) in order to get a good numerical scheme for solving the original problem. The efficiency of the introduced approach is illustrated on several numerical examples. Results are compared on several iterative methods.
description: scientific article; zbMATH DE number 6043443