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Two-step modulus-based matrix splitting iteration method for linear complementarity problems

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Abstract

Bai has recently presented a modulus-based matrix splitting iteration method, which is a powerful alternative for solving the large sparse linear complementarity problems. In this paper, we further present a two-step modulus-based matrix splitting iteration method, which consists of a forward and a backward sweep. Its convergence theory is proved when the system matrix is an H  + -matrix. Moreover, for the two-step modulus-based relaxation iteration methods, more exact convergence domains are obtained without restriction on the Jacobi matrix associated with the system matrix, which improve the existing convergence theory. Numerical results show that the two-step modulus-based relaxation iteration methods are superior to the modulus-based relaxation iteration methods for solving the large sparse linear complementarity problems.

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  1. State Key Laboratory of Scientific/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

    Li-Li Zhang

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Zhang, LL. Two-step modulus-based matrix splitting iteration method for linear complementarity problems. Numer Algor 57, 83–99 (2011). https://doi.org/10.1007/s11075-010-9416-7

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  • DOI: https://doi.org/10.1007/s11075-010-9416-7

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