Preconditioned AHSS iteration method for singular saddle point problems

Preconditioned AHSS iteration method for singular saddle point problems

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Article ID: iaor20134204
Volume: 63
Issue: 3
Start Page Number: 521
End Page Number: 535
Publication Date: Jul 2013
Journal: Numerical Algorithms
Authors: ,
Keywords: iterative methods, singularity
Abstract:

In this paper, for solving the singular saddle point problems, we present a new preconditioned accelerated Hermitian and skew‐Hermitian splitting (AHSS) iteration method. The semi‐convergence of this method and the eigenvalue distribution of the preconditioned iteration matrix are studied. In addition, we prove that all eigenvalues of the iteration matrix are clustered for any positive iteration parameters α and β. Numerical experiments illustrate the theoretical results and examine the numerical effectiveness of the AHSS iteration method served either as a preconditioner or as a solver.

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