Constraint preconditioning for nonsymmetric indefinite linear systems |
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Authors: | Li‐Ying Sun Jun Liu |
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Affiliation: | 1. Department of Mathematics, Guangdong Education Institute, Guangzhou 510303, People's Republic of China;2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People's Republic of China |
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Abstract: | 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. |
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Keywords: | preconditioning indefinite matrices minimum polynomial Schilders' factorization |
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