Efficient Evaluation of Large Polynomials
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Leiserson_Efficient evaluation.pdf
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Author(s)
Leiserson, Charles E.
Li, Liyun
Maza, Marc Moreno
Xie, Yuzhen
Date Issued
September 2010
Journal
Mathematical Software – ICMS 2010
Publisher
Springer-Verlag
Citation
Leiserson, Charles E., Liyun Li, Marc Moreno Maza, and Yuzhen Xie. "Efficient Evaluation of Large Polynomials." K. Fukuda et al. (Eds.): Mathematical Software – ICMS 2010, Lecture Notes in Computer Science, Volume 6327, 2010, pp. 342-353.
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Author's final manuscript
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) [superscript O(1)] bit operations plus dt [superscript O(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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1007/978-3-642-15582-6_55
