TY - JOUR
T1 - A Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 102
EP - 121
PY - 2019
DA - 2019/01
SN - 9
DO - http://doi.org/10.4208/eajam.020318.220618
UR - https://global-sci.org/intro/article_detail/eajam/12937.html
KW - Linear complementarity problem, matrix splitting, iteration method, relaxation, convergence.
AB - <p style="text-align: justify;">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 $ω_1$&nbsp;and $ω_2$<sub>&nbsp;</sub>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.</p>