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

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