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A generalization of the HSS-based sequential two-stage method for solving non-Hermitian saddle point problems

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Abstract

For non-Hermitian saddle point problems with non-Hermitian positive definite (1,1)-block, Zhu et al. studied the HSS-based sequential two-stage method (see Zhu et al. Appl. Math. Comput. 242, 907–916 19). However, this approach may not work when the (1,1)-block of the saddle point problems is weakly Hermitian or skew-Hermitian dominant. By introducing a new preconditioning matrix, a generalization of the HSS-based sequential two-stage method is proposed for solving non-Hermitian saddle-point problems with non-Hermitian positive definite and Hermitian or skew-Hermitian dominant (1,1)-block. Theoretical analysis shows that the proposed iterative method is convergent. Numerical experiments are provided to confirm the theoretical results, which demonstrate that the generalized method is effective and feasible for solving saddle point problems with non-Hermitian positive definite and Hermitian or skew-Hermitian dominant (1,1)-block.

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Authors and Affiliations

  1. School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou, 350007, China

    Cairong Chen & Changfeng Ma

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  1. Cairong Chen
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  2. Changfeng Ma
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Correspondence to Changfeng Ma.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11071041), Fujian Natural Science Foundation (Grant Nos. 2016J01005,2015J01578) and R&D of Key Instruments and Technologies for Deep Resources Prospecting (the National R&D Projects for Key Scientific Instruments) under grant number ZDYZ2012-1-02-04.

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Chen, C., Ma, C. A generalization of the HSS-based sequential two-stage method for solving non-Hermitian saddle point problems. Numer Algor 73, 1073–1090 (2016). https://doi.org/10.1007/s11075-016-0130-y

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