Modified overrelaxed iterative solution schemes for separable generalized equations

We formulate and analyze modified overrelaxation schemes for the iterative solution of systems of linear equations, separable variational inequalities and, more generally, separable generalized equations. These schemes contain as special cases the classical linear overrelaxation methods and the nonlinear overrelaxation schemes previously studied by Cryer, Mangasarian and Uko. However, unlike the previous methods, the modified schemes are directly applicable to problems with zero diagonal entries. Our analysis also yields existence and uniqueness results for some of the generalized equations considered in the paper. (C) 2005 Elsevier Ltd. All rights reserved.