Efficient Evaluation of Large Polynomials
Author(s)Leiserson, Charles E.; Li, Liyun; Maza, Marc Moreno; Xie, Yuzhen
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Mathematical Software – ICMS 2010
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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