Vol. 53 No. 02 (2003): Volume 53 Number 02, June 2003
Articles

A parallel implementation of Chebyshev preconditioned conjugate gradient method

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  • Hasan DAĞ,
  • Çağatay AKÇADOĞAN
Hasan DAĞ
Computational Sience and Engineering Program, Informatics Institute, Istanbul Technical University
Çağatay AKÇADOĞAN
Computational Sience and Engineering Program, Informatics Institute, Istanbul Technical University

Published 2003-09-01

Keywords

  • Chebyshev polynomials,
  • conjugate gradient method,
  • iterative methods,
  • preconditioner

How to Cite

DAĞ, Hasan, and Çağatay AKÇADOĞAN. 2003. “A Parallel Implementation of Chebyshev Preconditioned Conjugate Gradient Method”. ITU ARI Bulletin of Istanbul Technical University 53 (02):13-21. https://ari.itu.edu.tr/index.php/ituari/article/view/35.

Copyright (c) 2003 ITU Press

Creative Commons License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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 mainly matrix-vector and matrix-matrix multiplications, convincing results are obtained in terms of both speed and scalability.
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