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A note on semi-convergence of generalized parameterized inexact Uzawa method for singular saddle point problems

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Abstract

Recently, Zhang and Wang studied the generalized parameterized inexact Uzawa (GPIU) method for singular saddle point problems, see Zhang and Wang (Appl. Math. Comput. 219:4225–4231, 2013). In this note, we prove the semi-convergence of GPIU method by another method, which has weaken the conditions of GPIU method. Then, we analyze the spectral properties of the corresponding preconditioned matrix. Moreover, for solving singular saddle point problems, we give a preconditioned matrix for GPIU method, numerical experiments are given to illustrate the efficiency of GPIU method with the preconditioned matrix.

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200241, People’s Republic of China

    Zhen Chao & Guoliang Chen

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  1. Zhen Chao
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  2. Guoliang Chen
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Correspondence to Guoliang Chen.

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This work is supported by the National Natural Science Foundation of China (No. 11071079)

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Chao, Z., Chen, G. A note on semi-convergence of generalized parameterized inexact Uzawa method for singular saddle point problems. Numer Algor 68, 95–105 (2015). https://doi.org/10.1007/s11075-014-9840-1

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