Efficient Evaluation of Large Polynomials

  • Charles E. Leiserson
  • Liyun Li
  • Marc Moreno Maza
  • Yuzhen Xie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)

Abstract

Minimizing the evaluation cost of a polynomial expression is a fundamental problem in computer science. We propose tools that, for a polynomial P given as the sum of its terms, compute a representation that permits a more efficient evaluation. Our algorithm runs in d(nt)O(1) bit operations plus dtO(1) operations in the base field where d, n and t are the total degree, number of variables and number of terms of P. Our experimental results show that our approach can handle much larger polynomials than other available software solutions. Moreover, our computed representation reduce the evaluation cost of P substantially.

Keywords

Multivariate polynomial evaluation code optimization Cilk++ 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Charles E. Leiserson
    • 1
  • Liyun Li
    • 2
  • Marc Moreno Maza
    • 2
  • Yuzhen Xie
    • 2
  1. 1.CSAILMassachussets Institute of TechnologyCambridgeUSA
  2. 2.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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