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Overlapping restricted additive Schwarz method applied to the linear complementarity problem with an H-matrix

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Abstract

In this paper, a restricted additive Schwarz method is introduced for solving the linear complementarity problem that involves an H +-matrix. We show that the sequence generated by the restricted additive Schwarz method converges to the unique solution of the problem without any restriction on the initial point. Moreover, the comparison theorem is given between different versions of the restricted additive Schwarz method by using the weighted max-norm. We also show that the restricted additive Schwarz method is much better than the corresponding additive Schwarz variants in terms of the iteration number and the execution time.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082, P.R. China

    Haijian Yang & Qingguo Li

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  1. Haijian Yang
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  2. Qingguo Li
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Correspondence to Qingguo Li.

Additional information

The work is supported by the National Nature Science Foundation (No. 10771056) and the National High Technology Research and Development Program (No. 2006AA04A104), P.R. China.

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Yang, H., Li, Q. Overlapping restricted additive Schwarz method applied to the linear complementarity problem with an H-matrix. Comput Optim Appl 51, 223–239 (2012). https://doi.org/10.1007/s10589-010-9334-6

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  • DOI: https://doi.org/10.1007/s10589-010-9334-6

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