A parallel implementation of Chebyshev preconditioned conjugate gradient method

Akcadogan C., Dag H.

2nd International Symposium on Parallel and Distributed Computing (ISPDC 2003), Ljubljana, Slovenia, 13 - 14 October 2003, pp.1-8 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1109/ispdc.2003.1267636
  • City: Ljubljana
  • Country: Slovenia
  • Page Numbers: pp.1-8
  • Istanbul Technical University Affiliated: No

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.