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 dt 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.
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Leiserson, C.E., Li, L., Maza, M.M., Xie, Y. (2010). Efficient Evaluation of Large Polynomials. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_55
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DOI: https://doi.org/10.1007/978-3-642-15582-6_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15581-9
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