Convergence of Iterates of an Inexact Matrix Splitting Algorithm for the Symmetric Monotone Linear Complementarity Problem

Convergence of iterates is established for a symmetric regular matrix splitting algorithm for the solution of the symmetric monotone linear complementarity problem where the subproblems are solved inexactly. The notable iterate convergence recently established by Luo and Tseng for exact subproblem solution is extended here to inexact subproblem solution for a symmetric matrix splitting. A principal application of the present result is to iterate convergence for the inexact block Jacobi method for which Pang and Yang established convergence of a subsequence of the iterates.