Solving Nonlinear Matrix Equations on a Hypercube

Abstract

Nonlinear matrix equations arise frequently in applied probability, especially in the numerical solution of many stochastic models in queueing, inventory, communications, and dam theories. Due to the huge amount of computations involved in these nonlinear matrix equations, the existing algorithms for the solutions have not been satisfactory. With the advent of parallel computers, the door is open for efficient parallel algorithms to tackle the problem. This paper is an effort in this direction. A parallel algorithm on distributed computer systems is devised, and numerical experiment is done on the hypercube.