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Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems

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Abstract

In order to solve large sparse linear complementarity problems on parallel multiprocessor systems, we construct modulus-based synchronous two-stage multisplitting iteration methods based on two-stage multisplittings of the system matrices. These iteration methods include the multisplitting relaxation methods such as Jacobi, Gauss–Seidel, SOR and AOR of the modulus type as special cases. We establish the convergence theory of these modulus-based synchronous two-stage multisplitting iteration methods and their relaxed variants when the system matrix is an H  + -matrix. Numerical results show that in terms of computing time the modulus-based synchronous two-stage multisplitting relaxation methods are more efficient than the modulus-based synchronous multisplitting relaxation methods in actual implementations.

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Authors and Affiliations

  1. State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100190, People’s Republic of China

    Zhong-Zhi Bai & Li-Li Zhang

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  1. Zhong-Zhi Bai
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  2. Li-Li Zhang
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Correspondence to Zhong-Zhi Bai.

Additional information

Supported by The National Natural Science Foundation for Creative Research Groups (No. 11021101), The Hundred Talent Project of Chinese Academy of Sciences, The National Basic Research Program (No. 2011CB309703), and The National Natural Science Foundation (No. 91118001), People’s Republic of China.

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Bai, ZZ., Zhang, LL. Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numer Algor 62, 59–77 (2013). https://doi.org/10.1007/s11075-012-9566-x

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  • DOI: https://doi.org/10.1007/s11075-012-9566-x

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