Department of Applied Mathematics & Physics, Kyoto Univiversity
Technical Report #99014 (July, 1999)
Weighted Max-Norm Estimate of Additive Schwarz Iteration Scheme for Solving Linear Complementarity Problems
by Jin-Ping Zeng, Dong-Hui Li and Masao Fukushima
In this paper, we consider an algebraic additive Schwarz iteration scheme for
solving the finite-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.