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Parallel algorithms for solving certain classes of linear recurrences

  • S. Lakshmivarahan
  • Sudarshan K. Dhall
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 206)

Abstract

This paper presents two new time and/or processor bounds for solving certain classes of linear recurrences. The first result provides a parallel algorithm for solving Xi=aiXi−1+di for 1≤i≤n in 210gn units of time using only 3/4n processors. The second results relate to solving Xi=Xi−1+Xi−2+di for 1≤i≤n. It is shown that Xi's can be computed in at most 310gn units of time using 5/4n processors. In the special case when di=0 for all i, it is shown that Xi's (the first n-Fibonacci numbers) can be computed in parallel in 210gn-1 units of time using only n/2 processors. These time and processor bounds compare very favourably with the previously known results for these problems.

Keywords

Parallel Algorithm Fibonacci Number Linear Recurrence Cyclic Reduction Tridiagonal Linear System 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • S. Lakshmivarahan
    • 1
  • Sudarshan K. Dhall
    • 1
  1. 1.Parallel Processing Institute School of Electrical Engineering and Computer ScienceUniversity of OklahomaNorman

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