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The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems

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Abstract

Recently, Li and Wu (2015) proposed the single-step Hermitian and skew-Hermitian splitting (SHSS) method for solving the non-Hermitian positive definite linear systems. Based on the single-step Hermitian and skew-Hermitian splitting of the (1,1) part of the saddle-point coefficient matrix, a new Uzawa-type method is proposed for solving a class of saddle-point problems with non-Hermitian positive definite (1,1) parts. Convergence (Semi-convergence) properties of this new method for nonsingular (singular) are derived under suitable conditions. Numerical examples are implemented to confirm the theoretical results and verify that this new method is more feasibility and robustness than the new HSS-like (NHSS-like), the Uzawa-HSS and the parameterized Uzawa-skew-Hermitian triangular splitting (PU-STS) methods for solving both the nonsingular and the singular saddle-point problems with non-Hermitian positive definite and Hermitian dominant (1,1) parts.

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Acknowledgments

We would like to express our sincere thanks to the anonymous reviewers for their valuable suggestions which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, People’s Republic of China

    Zhengge Huang, Ligong Wang, Zhong Xu & Jingjing Cui

Authors
  1. Zhengge Huang
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  2. Ligong Wang
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  3. Zhong Xu
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  4. Jingjing Cui
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Corresponding author

Correspondence to Ligong Wang.

Additional information

Communicated by Andreas Fischer.

This work is supported by the National Natural Science Foundations of China (No. 11171273) and sponsored by Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (No. CX201628).

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Huang, Z., Wang, L., Xu, Z. et al. The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems. Comp. Appl. Math. 37, 1213–1231 (2018). https://doi.org/10.1007/s40314-016-0390-0

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  • DOI: https://doi.org/10.1007/s40314-016-0390-0

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