On the use of rational iterative methods for solving large sparse linear systems

In this paper the authors describe some work which is being carried on in the Center for Numerical Analysis at The University of Texas at Austin on the development of effective iterative procedures for solving large sparse linear systems. They are primarily interested in linear systems arising from the solution of elliptic partial different equations by finite difference methods. The object of the work is to develop iterative procedures which are not only rapidly convergent but which are also suited for use on vector and parallel supercomputers.