Elsevier

Applied Mathematics Letters

Volume 79, May 2018, Pages 205-210
Applied Mathematics Letters

On a type of matrix splitting preconditioners for a class of block two-by-two linear systems

https://doi.org/10.1016/j.aml.2017.12.020Get rights and content
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Abstract

Recently, Bai et al. (2013) proposed an effective and efficient matrix splitting iterative method, called preconditioned modified Hermitian/skew-Hermitian splitting (PMHSS) iteration method, for two-by-two block linear systems of equations. The eigenvalue distribution of the iterative matrix suggests that the splitting matrix could be advantageously used as a preconditioner. In this study, the CGNR method is utilized for solving the PMHSS preconditioned linear systems, and the performance of the method is considered by estimating the condition number of the normal equations. Furthermore, the proposed method is compared with other PMHSS preconditioned Krylov subspace methods by solving linear systems arising in complex partial differential equations and a distributed control problem. The numerical results demonstrate the difference in the performance of the methods under consideration.

Keywords

PMHSS preconditioner
Krylov subspace method
Two-by-two block matrix
Matrix splitting

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