A modified modulus method for symmetric positive‐definite linear complementarity problems |
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| Authors: | Jun‐Liang Dong Mei‐Qun Jiang |
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| Affiliation: | 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 100080, People's Republic of China;2. Permanent address: College of Applied Sciences, Beijing University of Technology, Beijing 100124, People's Republic of China.;3. School of Mathematical Sciences, Suzhou University, Suzhou 215006, People's Republic of China |
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| Abstract: | By reformulating the linear complementarity problem into a new equivalent fixed‐point equation, we deduce a modified modulus method, which is a generalization of the classical one. Convergence for this new method and the optima of the parameter involved are analyzed. Then, an inexact iteration process for this new method is presented, which adopts some kind of iterative methods for determining an approximate solution to each system of linear equations involved in the outer iteration. Global convergence for this inexact modulus method and two specific implementations for the inner iterations are discussed. Numerical results show that our new methods are more efficient than the classical one under suitable conditions. Copyright © 2008 John Wiley & Sons, Ltd. |
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| Keywords: | linear complementarity problem system of linear equations modulus method inexact iterative method symmetric positive‐definite matrix |
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