Weighted Max-Norm Estimate of Additive Schwarz Iteration Scheme for Solving Linear Complementarity Problems

In this paper, we consider an algebraic additive Schwarz iteration scheme for solving the nite-dimensional linear complementarity problem that involves an M-matrix. The scheme contains some existing algorithms as special cases. We establish monotone convergence of the iteration scheme under appropriate conditions. Moreover, using the concept of weak regular splitting, we estimate weighted max-norm bounds for iteration errors; thereby we show that the sequence generated by the iteration scheme converges to the unique solution of the problem without any restriction on the initial point. The work of the rst two authors was done while they were visiting Kyoto University.