A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

Year:    2019

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 1 : pp. 102–121

Abstract

A general RTMS iteration method for linear complementarity problems is proposed. Choosing various pairs of relaxation parameters, we obtain new two-sweep modulus-based matrix splitting iteration methods and already known iteration procedures such as the MS [1] and TMS [27] iteration methods. If the system matrix is positive definite or an $H_+$-matrix and the relaxation parameters $ω_1$ and $ω_2$ satisfy the inequality 0≤$ω_1$, $ω_2$≤1, sufficient conditions for the uniform convergence of MS, TMS and NTMS iteration methods are established. Numerical results show that with quasi-optimal parameters, RTMS iteration method outperforms MS and TMS iteration methods in terms of computing efficiency.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.020318.220618

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 1 : pp. 102–121

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Linear complementarity problem matrix splitting iteration method relaxation convergence.

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