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On generalized parameterized inexact Uzawa methods for singular saddle-point problems

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Abstract

For a class of nonsingular saddle-point problems, Bai et al. in 2008 studied an efficient parameterized inexact Uzawa (PIU) method; see [Z.-Z. Bai, Z.-Q. Wang, On parameterized inexact Uzawa methods for generalized saddle-point problems, Linear Algebra Appl. 428 (2008) 2900–2932]. In this paper, we use a generalized version of the PIU method, named as generalized PIU (GPIU) method, to solve the singular saddle-point problems. The semi-convergence properties of the GPIU method are derived under suitable restrictions on the involved iteration parameters. Moreover, the quasi-optimal iteration parameters and the corresponding quasi-optimal semi-convergence factor are also determined. Numerical experiments are used to verify the feasibility and effectiveness of the GPIU method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Ai-Li Yang, Yan Dou & Yu-Jiang Wu

  2. Key Laboratory of Applied Mathematics and Complex Systems, Gansu Province, Lanzhou, 730000, People’s Republic of China

    Ai-Li Yang, Yan Dou & Yu-Jiang Wu

  3. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, 730050, People’s Republic of China

    Xu Li

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  1. Ai-Li Yang
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  2. Yan Dou
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  4. Xu Li
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Correspondence to Ai-Li Yang.

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Yang, AL., Dou, Y., Wu, YJ. et al. On generalized parameterized inexact Uzawa methods for singular saddle-point problems. Numer Algor 69, 579–593 (2015). https://doi.org/10.1007/s11075-014-9914-0

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  • DOI: https://doi.org/10.1007/s11075-014-9914-0

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