Efficient evaluation of large polynomials

Authors:
Charles E. Leiserson;Liyun Li;Marc Moreno Maza;Yuzhen Xie
Affiliations:
CSAIL, Massachussets Institute of Technology, Cambridge, MA;Department of Computer Science, University of Western Ontario, London, ON, Canada;Department of Computer Science, University of Western Ontario, London, ON, Canada;Department of Computer Science, University of Western Ontario, London, ON, Canada
Venue:
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Year:
2010

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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.