Skip to main content
SpringerLink
Log in

A Parallel Solver for Circulant Toeplitz Tridiagonal Systems on Hypercubes

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

Solving circulant Toeplitz tridiagonal systems arises in many engineering applications. This paper presents a fast parallel algorithm for solving this type of systems. The number of floating-point operations required in our algorithm is less than the previous parallel algorithm [cf. Kim and Lee (1990)] for solving the similar system. Specifically, an overlapping technique is proposed to reduce the communication steps required. In addition, an error analysis is given. The implementation of our algorithm on the nCUBE2/E with 16 processors has been carried out. The experimental results show that the speedup is almost linearly proportional to the number of processors.

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

  • Hockney, R. W. (1965). A fast direct solution of Poisson's equation using Fourier analysis. J. ACM 12, 95–113.

    Google Scholar 

  • Widlund, O. B. (1972). On the use of fast methods for separable finite difference equations for the solution of general elliptic problems, in Sparse Matrices and Their Applications, Rose, D. J., and Willoughby, R. A. (eds.), Plenum Press, New York, pp. 121–131.

    Google Scholar 

  • Fisher, D., Golub, G., Hald, O., Levia, C., and Winlund, O. (1974). On Fourier-Toeplitz methods for separable elliptic problems. Mathematics of Computation 28, 349–368.

    Google Scholar 

  • Smith, G. D. (1985). Numerical Solution of Partial Differential Equations: Finite Difference Methods, Third Edition, Oxford University Press.

  • Chung, K. L., and Yan, W. M. (1994). A fast algorithm for cubic B-spline curve fitting. Comput. Graphics 18(3), 327–334.

    Google Scholar 

  • Hirsh, R. (1975). Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique. J. Comput. Phy. 19, 90–109.

    Google Scholar 

  • Yan, W. M., and Chung, K. L. (1994). A fast algorithm for solving special tridiagonal systems, Computing 52, 203–211.

    Google Scholar 

  • Ranka, S., and Sahni, S. (1990). Hupercube Algorithms with Applications to Image Processing and Pattern Recognition, Springer-Verlag, Chap. 2, pp. 29–30.

  • nCUBE Company, (1993). nCUBE 2 Processor Manual, Foster City, California.

  • nCUBE Company, (1993). nCUBE 2 Programmer's Guide, Foster City, California.

  • Kim, H. J., and Lee, J. G. (1990). A parallel algorithm solving a tridiagonal Toeplitz linear system, Parallel Computing 13, 289–294.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information and Computer Education, National Taiwan Normal University, Taipei, 10610, Taiwan R. O. C.

    Jung-Gen Wu & Kuo-Liang Chung

  2. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, 10764, Taiwan R. O. C.

    Wen-Ming Yan

Authors
  1. Jung-Gen Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen-Ming Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kuo-Liang Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kuo-Liang Chung.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, JG., Yan, WM. & Chung, KL. A Parallel Solver for Circulant Toeplitz Tridiagonal Systems on Hypercubes. Journal of Scientific Computing 12, 409–431 (1997). https://doi.org/10.1023/A:1025629029872

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025629029872

Search

Navigation