The alternating group explicit (AGE) matrix iterative method

It is well known that iterative methods, utilizing the great speed of modern computers, are extensively used in large-scale computations for solving matrix equations which arise from finite difference approxmations to elliptic partial differential equations. The object of this paper is to introduce a new explicit iterative method suitable for parallel computation for the solution of the associated matrix equations and compare its performance with existing methods (Jacobi, successive over-relaxation). It is hoped that numerical experiments on the simple one-dimensional linear model and its extensions to multi-dimensional problems will serve as an indication of the power of the new (AGE) matrix iterative method.