Inexact Parallel Relaxed Multisplitting Algorithm for Linear Complementarity Problem

In this paper, the authors first 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 specific 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 coefficient matrix is an H-matrix with positive diagonal elements. Last, a specific iteration form for this inexact multisplitting Algorithm is presented, where the inner iterations are implemented through a matrix splitting method. Convergence properties for this specific form are analyzed.