East Asian J. Appl. Math., 9 (2019), pp. 102-121.
Published online: 2019-01
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020318.220618}, url = {http://global-sci.org/intro/article_detail/eajam/12937.html} }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.