A splitting preconditioner for saddle point problems |
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Authors: | Yang Cao Mei‐Qun Jiang Ying‐Long Zheng |
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Affiliation: | School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu 215006, People's Republic of China |
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Abstract: | For large sparse systems of linear equations iterative techniques are attractive. In this paper, we study a splitting method for an important class of symmetric and indefinite system. Theoretical analyses show that this method converges to the unique solution of the system of linear equations for all t>0 (t is the parameter). Moreover, all the eigenvalues of the iteration matrix are real and nonnegative and the spectral radius of the iteration matrix is decreasing with respect to the parameter t. Besides, a preconditioning strategy based on the splitting of the symmetric and indefinite coefficient matrices is proposed. The eigensolution of the preconditioned matrix is described and an upper bound of the degree of the minimal polynomials for the preconditioned matrix is obtained. Numerical experiments of a model Stokes problem and a least‐squares problem with linear constraints presented to illustrate the effectiveness of the method. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | saddle point problems iterative method convergence preconditioning |
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