Modulus‐based matrix splitting iteration methods for linear complementarity problems |
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Authors: | Zhong‐Zhi Bai |
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Institution: | 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 |
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Abstract: | For the large sparse linear complementarity problems, by reformulating them as implicit fixed‐point equations based on splittings of the system matrices, we establish a class of modulus‐based matrix splitting iteration methods and prove their convergence when the system matrices are positive‐definite matrices and H+‐matrices. These results naturally present convergence conditions for the symmetric positive‐definite matrices and the M‐matrices. Numerical results show that the modulus‐based relaxation methods are superior to the projected relaxation methods as well as the modified modulus method in computing efficiency. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | linear complementarity problem matrix splitting iteration method convergence |
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