A parallel implementation of Chebyshev preconditioned conjugate gradient method

Authors:
Çağatay Akçadoğan;Hasan Dağ
Affiliations:
Computational Science and Engineering Program, Informatics Institute, Istanbul Technical University, Istanbul, Turkey;Computational Science and Engineering Program, Informatics Institute, Istanbul Technical University, Istanbul, Turkey
Venue:
ISPDC'03 Proceedings of the Second international conference on Parallel and distributed computing
Year:
2003

Citing 3
Cited 1

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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.