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. © 2010 Springer Science+Business Media, LLC.

On preconditioned MHSS iteration methods for complex symmetric linear systems

Benzi, Michele;
2011

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. © 2010 Springer Science+Business Media, LLC.
2011
Complex symmetric linear system; Convergence theory; MHSS iteration; Preconditioning; Spectral properties; Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/75291
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