On the convergence of modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems with \(H_+\)-matrices (Q1639538)

The authors present a class of modulus-based matrix splitting iteration methods and extend the convergence theory from the H-compatible splitting to \(H\)-splitting for a class of nonlinear complementarity problems. Practical choices of parameters in the implementations are studied, so that the obtained convergence domain is larger than the existing results. The convergence theory is extended from the \(H\)-compatible splitting to \(H\)-splitting when the matrix is an \(H_+\)-matrix. Some numerical examples are presented to support the theoretical results and to illustrate the efficiency of the proposed methods.