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Constraint preconditioning for nonsymmetric indefinite linear systems
Author(s) -
Sun LiYing,
Liu Jun
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.664
Subject(s) - preconditioner , krylov subspace , mathematics , generalized minimal residual method , eigenvalues and eigenvectors , factorization , incomplete lu factorization , polynomial , saddle point , matrix decomposition , linear system , upper and lower bounds , matrix (chemical analysis) , dimension (graph theory) , subspace topology , mathematical analysis , algorithm , pure mathematics , physics , geometry , materials science , quantum mechanics , composite material
This paper introduces and presents theoretical analyses of constraint preconditioning via a Schilders'‐like factorization for nonsymmetric saddle‐point problems. We extend the Schilders' factorization of a constraint preconditioner to a nonsymmetric matrix by using a different factorization. The eigenvalue and eigenvector distributions of the preconditioned matrix are determined. The choices of the parameter matrices in the extended Schilders' factorization and the implementation of the preconditioning step are discussed. An upper bound on the degree of the minimum polynomial for the preconditioned matrix and the dimension of the corresponding Krylov subspace are determined, as well as the convergence behavior of a Krylov subspace method such as GMRES. Numerical experiments are presented. Copyright © 2009 John Wiley & Sons, Ltd.