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The numerous applications of the linear complementarity problem (LCP) in, e.g., the solution of linear and convex quadratic programming, free boundary value problems of fluid mechanics, and moving boundary value problems of economics make its efficient numerical solution a very imperative and interesting area of research. For the solution of the LCP, many iterative methods have been proposed, especially, when the matrix of the problem is a real positive definite or an H+- matrix. In this work we assume that the real matrix of the LCP is an H+-matrix and solve it by using a new method, the scaled extrapolated block modulus algorithm, as well as an improved version of the very recently introduced modulus-based matrix splitting modified AOR iteration method. As is shown by numerical examples, the two new methods are very effective and competitive with each other. [ABSTRACT FROM AUTHOR]

In the last four decades many articles have been devoted to the modifications and improvements of classes of preconditioners for linear systems whose matrix coefficient is an M-matrix in order to improve on the convergence rates of the classical iterative schemes (Jacobi, Gauss–Seidel, etc.). The present work is a contribution towards the generalization of the most common preconditioners used so far. [Copyright &y& Elsevier]