An iterative method for large sparse linear systems on a vector computer

In this paper we consider the arithmetic mean method for solving large sparse systems of linear equations. This iterative method converges for systems with coefficient matrices that are symmetric positive definite or positive real or irreducible L-matrices with a strong diagonal dominance. The method is very suitable for parallel implementation on a multiprocessor system, such as the CRAY X-MP. Some numerical experiments on systems resulting from the discretization, by means of the usual 5-point difference formulae, of an elliptic partial differential equation are presented