On the choice of parameters in MAOR type splitting methods for the linear complementarity problem

Abstract

In the present work we consider the iterative solution of the Linear Complementarity Problem (LCP), with a nonsingular H (+) coefficient matrix A, by using all modulus-based matrix splitting iterative methods that have been around for the last couple of years. A deeper analysis shows that the iterative solution of the LCP by the modified Accelerated Overrelaxation (MAOR) iterative method is the "best", in a sense made precise in the text, among all those that have been proposed so far regarding the following three issues: i) The positive diagonal matrix-parameter Omega a parts per thousand yen diag(A) involved in the method is Omega = diag(A), ii) The known convergence intervals for the two AOR parameters, alpha and beta, are the widest possible, and iii) The "best" possible MAOR iterative method is the modified Gauss-Seidel one.