<i>m</i>-Step Preconditioned Conjugate Gradient Methods

Abstract

This paper discusses preconditioners for the conjugate gradient method which are based on several iterations of stationary iterative methods. Necessary and sufficient conditions are given for the applicability of these preconditioners to symmetric and positive definite systems of linear equations. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.