A parallel implementation of chebyshev preconditioned conjugate gradient method

Abstract

A parallel implementation for linear set of equations of the form Ax = b is presented in this paper. In this implementation, instead of the traditional direct solution of Ax = b, conjugate gradient method is used. The conjugate gradient method is accelerated with an approximate inverse matrix preconditioner obtained from a linear combination of matrix-valued Chebyshev polynomials. This implementation is tested on a Sun SMP machine. Since conjugate gradient method and preconditioner contain only matrix-vector and matrix-matrix multiplications, convincing results are obtained in terms of both speed and scalability.