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A generalized preconditioned HSS method for singular saddle point problems

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Abstract

Li et al. recently studied the generalized HSS (GHSS) method for solving singular linear systems (see Li et al., J. Comput. Appl. Math. 236, 2338–2353 (2012)). In this paper, we generalize the method and present a generalized preconditioned Hermitian and skew-Hermitian splitting method (GPHSS) to solve singular saddle point problems. We prove the semi-convergence of GPHSS under some conditions, and weaken some semi-convergent conditions of GHSS, moreover, we analyze the spectral properties of the corresponding preconditioned matrix. Numerical experiments are given to illustrate the efficiency of GPHSS method with appropriate parameters both as a solver and as a preconditioner.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, People’s Republic of China

    Zhen Chao & Naimin Zhang

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  1. Zhen Chao
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  2. Naimin Zhang
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Correspondence to Naimin Zhang.

Additional information

This work is supported by Zhejiang Provincial Natural Science Foundation of China under grant No. Y1110451 and National Natural Science Foundation of China under grant No. 61002039.

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Chao, Z., Zhang, N. A generalized preconditioned HSS method for singular saddle point problems. Numer Algor 66, 203–221 (2014). https://doi.org/10.1007/s11075-013-9730-y

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