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Modulus‐based multigrid methods for linear complementarity problems |
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| Authors: | Zhong‐Zhi Bai Li‐Li Zhang |
| 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, Beijing, China;2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China;3. School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, China |
| Abstract: | By employing modulus‐based matrix splitting iteration methods as smoothers, we establish modulus‐based multigrid methods for solving large sparse linear complementarity problems. The local Fourier analysis is used to quantitatively predict the asymptotic convergence factor of this class of multigrid methods. Numerical results indicate that the modulus‐based multigrid methods of the W‐cycle can achieve optimality in terms of both convergence factor and computing time, and their asymptotic convergence factors can be predicted perfectly by the local Fourier analysis of the corresponding modulus‐based two‐grid methods. |
| Keywords: | asymptotic convergence factor linear complementarity problem local Fourier analysis modulus‐based matrix splitting iteration multigrid method |