Advertisement

Communication cost reduction for Krylov methods on parallel computers

  • E. de Sturler
  • H. A. van der Vorst
Numerical Algorithms for Engineering
Part of the Lecture Notes in Computer Science book series (LNCS, volume 797)

Abstract

On large distributed memory parallel computers the global communication cost of inner products seriously limits the performance of Krylov subspace methods [3]. We consider improved algorithms to reduce this communication overhead, and we analyze the performance by experiments on a 400-processor parallel computer and with a simple performance model.

Keywords

Communication Overhead Krylov Subspace Method Krylov Method Communication Cost Reduction Measured Runtimes 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Z. Bai, D. Hu, and L. Reichel. A Newton basis GMRES implementation. Technical Report 91-03, University of Kentucky, 1991.Google Scholar
  2. 2.
    J. W. Demmel, M. T. Heath, and H.A. van der Vorst. Parallel numerical linear algebra. Acta Numerica Vol 2, Cambridge Press, New York, 1993Google Scholar
  3. 3.
    E. De Sturler. A parallel restructured version of GMRES(m). Technical Report 91-85, Delft University of Technology, Delft, 1991.Google Scholar
  4. 4.
    E. De Sturler. A parallel variant of GMRES(m). In R. Vichnevetsky, J. H. H. Miller, editors, Proc. of the 13th IMACS World Congress on Computation and Applied Mathematics, IMACS, Criterion Press Dublin 1991, pp 682–683.Google Scholar
  5. 5.
    E. De Sturler and H. A. Van der Vorst. Reducing the effect of global communication in GMRES (m) and CG on Parallel Distributed Memory Computers. Technical Report 832, Mathematical Institute, University of Utrecht, Utrecht, 1993Google Scholar
  6. 6.
    M. R. Hestenes and E. Stiefel. Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand., 49:409–436, 1954.Google Scholar
  7. 7.
    Y. Saad and M. H. Schultz. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput., 7:856–869, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • E. de Sturler
    • 1
  • H. A. van der Vorst
    • 2
  1. 1.Swiss Scientific Computing Center CSCS-ETHZMannoSwitzerland
  2. 2.Mathematical InstituteUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations