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Improved PHSS iterative methods for solving saddle point problems

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Abstract

An improvement on a generalized preconditioned Hermitian and skew-Hermitian splitting method (GPHSS), originally presented by Pan and Wang (J. Numer. Methods Comput. Appl. 32, 174–182, 2011), for saddle point problems, is proposed in this paper and referred to as IGPHSS for simplicity. After adding a matrix to the coefficient matrix on two sides of first equation of the GPHSS iterative scheme, both the number of required iterations for convergence and the computational time are significantly decreased. The convergence analysis is provided here. As saddle point problems are indefinite systems, the Conjugate Gradient method is unsuitable for them. The IGPHSS is compared with Gauss-Seidel, which requires partial pivoting due to some zero diagonal entries, Uzawa and GPHSS methods. The numerical experiments show that the IGPHSS method is better than the original GPHSS and the other two relevant methods.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, People’s Republic of China

    Ke Wang & Jingjing Di

  2. Mathematics & Statistics and Mechanical Engineering, Louisiana Tech University, Ruston, LA, 71272, USA

    Don Liu

Authors
  1. Ke Wang
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  2. Jingjing Di
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  3. Don Liu
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Correspondence to Don Liu.

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Wang, K., Di, J. & Liu, D. Improved PHSS iterative methods for solving saddle point problems. Numer Algor 71, 753–773 (2016). https://doi.org/10.1007/s11075-015-0022-6

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  • DOI: https://doi.org/10.1007/s11075-015-0022-6

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