Supercomputing pp 563-575 | Cite as

A parallel block cyclic reduction algorithm for the fast solution of elliptic equations

  • E. Gallopoulos
  • Y. Saad
Session 6B: Parallel Numeric Methods
Part of the Lecture Notes in Computer Science book series (LNCS, volume 297)


This paper presents an adaptation of the Block Cyclic Reduction (BCR) algorithm for a multi-vector processor. The main bottleneck of BCR lies in the solution of linear systems whose coefficient matrix is the product of tridiagonal matrices. This bottleneck is handled by expressing the rational function corresponding to the inverse of this product as a sum of elementary fractions. As a result the solution of this system leads to parallel solutions of tridiagonal systems. Numerical experiments performed on an Alliant FX/8 are reported.


Fast Fourier Transform Outer Loop Matrix Polynomial Vector Length Elliptic Partial Differential Equation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • E. Gallopoulos
    • 1
  • Y. Saad
    • 1
  1. 1.Center for Supercomputing Research and DevelopmentUniversity of Illinois at Urbana ChampaignUrbanaU.S.A.

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