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THE GENERALIZED LOCAL HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHODS FOR THE NON-HERMITIAN GENERALIZED SADDLE POINT PROBLEMS

Hongtao Fan, Bing Zheng   

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
  • Received:2013-08-28 Revised:2014-01-15 Online:2014-05-15 Published:2014-05-22
  • Supported by:

    We would like to express our sincere gratitude to the anonymous referees whose constructive comments have the presentation of this paper greatly improved. The work was supported by the National Natural Science Foundation (No.11171371 and No.11101195).

Hongtao Fan, Bing Zheng. THE GENERALIZED LOCAL HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHODS FOR THE NON-HERMITIAN GENERALIZED SADDLE POINT PROBLEMS[J]. Journal of Computational Mathematics, 2014, 32(3): 312-331.

For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 (2012) 8816–8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting (GLHSS) iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the convergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.

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