Skip to main content
SpringerLink
Log in

Designing Optimal Algorithms for Solving Banded Triangular Systems on Rings

  • Published:
Journal of Mathematical Modelling and Algorithms

Abstract

Parallel complexity results for designing banded triangular solvers are provided. In particular, several lower bounds based on data layout and communication along a ring are derived based on solving such systems using substitution. Lastly, a near-optimal solver for a ring is discussed and provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Borodin, A. and Munro, I.: The Computational Complexity of Algebraic and Numeric Problems, Elsevier, New York, 1975.

    Google Scholar 

  2. Demmel, J. W., Heath, M. T. and van der Vorst, H. A.: Parallel numerical linear algebra, Technical Report UCB/CSD 93/703, University of California at Berkeley, 1993.

    Google Scholar 

  3. Eisenstat, S., Heath, M., Henkel, C. and Romine, C.: Modified cyclic algorithms for solving triangular systems on distributed memory multi-processors, SIAM J. Sci. Stat. Comput. (1988).

  4. Heath, M. T. and Romine, C. H.: Parallel solution of triangular systems on distributed-memory multiprocessors, SIAM J. Sci. Stat. Comput. (1988).

  5. Heller, D.: A survey of parallel algorithms in numerical linear algebra, SIAM J. Numer. Anal. 29(4) (1987).

  6. Higham, N.: Stability of parallel triangular system solvers, Numerical Analysis Report 236, University of Manchester, 1993.

  7. Karp, R. M. and Ramachandran, V. L.: Parallel algorithms for shared-memory machines, In: J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity,,Elsevier, Amsterdam, 1990, pp. 869–941. 180 EUNICE E. SANTOS ET AL.

    Google Scholar 

  8. Li, G. and Coleman, T.: A new method for solving triangular systems on distributed-memory message-passing multiprocessors, SIAM J. Sci. Stat. Comput. (1989).

  9. Romine, C. and Ortega, J.: Parallel solution of triangular systems of equations, Parallel Computing 6 (1988), 109–114.

    Google Scholar 

  10. Sameh, A. and Brent, R.: Solving triangular systems on a parallel computer, SIAM J. Numer. Anal. (1977).

  11. Santos, E. E.: On designing optimal parallel triangular solvers, Information Comput. 261(2) (2000).

  12. Santos, E. E., Santos, E., Jr. and Santos, E. S.: Designing optimal algorithms for solving banded triangular systems on rings, Technical Report No. LCID-02-107, Laboratory for Computation, Information, & Distributed Processing, Virginia Polytechnic Institute & State University, 2002.

Download references

Author information

Authors and Affiliations

  1. Department Computer Science, Virginia Polytechnic Institute & State University, Blacksburg, VA, 24061, U.S.A.

    Eunice E. Santos

  2. Department of Computer Science and Engineering, University of Connecticut, Storrs, CT, 06269, U.S.A.

    Eugene Santos Jr.

  3. Department of Computer Science and Information Systems, Youngstown State University, Youngstown, OH, 44555, U.S.A.

    Eugene S. Santos

Authors
  1. Eunice E. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eugene Santos Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eugene S. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Santos, E.E., Santos, E. & Santos, E.S. Designing Optimal Algorithms for Solving Banded Triangular Systems on Rings. Journal of Mathematical Modelling and Algorithms 1, 169–180 (2002). https://doi.org/10.1023/A:1020586405464

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020586405464

Search

Navigation