An improved block splitting preconditioner for complex symmetric indefinite linear systems

In this paper, an improved block splitting preconditioner for a class of complex symmetric indefinite linear systems is proposed. By adopting two iteration parameters and the relaxation technique, the new preconditioner not only remains the same computational cost with the block preconditioners but also is much closer to the original coefficient matrix. The theoretical analysis shows that the corresponding iteration method is convergent under suitable conditions and the preconditioned matrix can have well-clustered eigenvalues around (0,1) with a reasonable choice of the relaxation parameters. An estimate concerning the dimension of the Krylov subspace for the preconditioned matrix is also obtained. Finally, some numerical experiments are presented to illustrate the effectiveness of the presented preconditioner.

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