On preconditioned MHSS iteration methods for complex symmetric linear systems

On preconditioned MHSS iteration methods for complex symmetric linear systems

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Article ID: iaor20111400
Volume: 56
Issue: 2
Start Page Number: 297
End Page Number: 317
Publication Date: Feb 2011
Journal: Numerical Algorithms
Authors: , ,
Abstract:

We propose a preconditioned variant of the modified HSS (MHSS) iteration method for solving a class of complex symmetric systems of linear equations. Under suitable conditions, we prove the convergence of the preconditioned MHSS (PMHSS) iteration method and discuss the spectral properties of the PMHSS‐preconditioned matrix. Numerical implementations show that the resulting PMHSS preconditioner leads to fast convergence when it is used to precondition Krylov subspace iteration methods such as GMRES and its restarted variants. In particular, both the stationary PMHSS iteration and PMHSS‐preconditioned GMRES show meshsize‐independent and parameter‐insensitive convergence behavior for the tested numerical examples.

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