Inexact Parallel Relaxed Multisplitting Algorithm for Linear Complementarity Problem

Abstract

In this paper, the authors ¿rst set up the inexact parallel relaxed multisplitting Algorithm for solving the linear complementarity problems, which is based on the inexact splitting method, parallel computation and the multisplitting method. This new Algorithm provides a speci¿c realization for the multisplitting method and generalizes many existing matrix splitting methods for linear complementarity problems. And then, the global convergence theory of this new Algorithm is proved when the coef¿cient matrix is an H−matrix with positive diagonal elements. Last, a speci¿c iteration form for this inexact multisplitting Algorithm is presented, where the inner iterations are implemented through a matrix splitting method. Convergence properties for this speci¿c form are analyzed.