On preconditioned MHSS iteration methods for complex symmetric linear systems. (English) Zbl 1209.65037

Bai, Zhong-Zhi; Benzi, Michele; Chen, Fang

Numer. Algorithms 56, No. 2, 297-317 (2011).

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.

Reviewer: Dietrich Braess (Bochum)

MSC:

65F10	Iterative numerical methods for linear systems
65F08	Preconditioners for iterative methods

Keywords:

complex symmetric linear system; MHSS iteration; preconditioning; convergence Krylov subspace iteration methods; GMRES; numerical examples

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