Parallel algorithms for solving linear recurrence systems

  • Przemysław Stpiczyński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 634)


We present two parallel algorithms for solving linear recurrence systems Rn,m〉 where m is relatively small, which can be simply implemented on message passing multiprocessors. Theorems concerning their time complexity are also given together with the criterion when each of them should be used. If m is O(1) then the algorithms are effective.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Borodin, I. Munro: The computational complexity of algebraic and numerical problems. New York:American Elsevier 1975Google Scholar
  2. 2.
    S.-C. Chen: Speedup of iterative programs in multiprocessing systems. Dissertation. Dept. of Computer Sci., University of Illinois Urbana 1975Google Scholar
  3. 3.
    S.-C. Chen, D.J. Kuck: Time and parallel processor bounds for linear recurrence systems. IEEE Trans. on Computers 24, 701–717 (1975)Google Scholar
  4. 4.
    M. Cosnard, B. Tourancheau, G. Villard: Gaussian elimination on message passing architecture. In E.N. Houstis et al. (eds.): Supercomputing. Lecture Notes in Computer Science 297. Berlin: Springer 1988. pp. 611–628Google Scholar
  5. 5.
    D. Heller: A survey of parallel algorithms in numerical linear algebra. SIAM Review 20, 740–777 (1978)CrossRefGoogle Scholar
  6. 6.
    L. Hyafil, H.T. Kung: The complexity of parallel evaluation of linear recurrences. Journal of ACM 24, 513–521 (1977)CrossRefGoogle Scholar
  7. 7.
    D.J. Kuck: Structure of Computers and Computations. New York: Wiley 1978Google Scholar
  8. 8.
    J. Modi: Parallel Algorithms and Matrix Computations. Oxford: Oxford University Press 1988Google Scholar
  9. 9.
    Y. Robert, B. Tourancheau, G. Villard: Data allocation strategies for Gauss and Jordan algorithms on a ring of processors. Inf. Proc. Letters 31, 21–29 (1989)Google Scholar
  10. 10.
    A.H. Sameh, R.P. Brent: Solving triangular systems on a parallel computer. SIAM J. Numer. Anal. 14, 1101–1113 (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Przemysław Stpiczyński
    • 1
  1. 1.Numerical Analysis DepartmentMarie Curie-Sklodowska UniversityLublinPoland

Personalised recommendations