UWSpace will be migrating to a new version of its software from July 29th to August 1st. UWSpace will be offline for all UW community members during this time.
On the evaluation of some sparse polynomials
dc.contributor.author | Schost, Eric | |
dc.contributor.author | Nogneng, Dorian | |
dc.contributor.author | Nogneng, Dorian | |
dc.date.accessioned | 2023-03-21 19:03:04 (GMT) | |
dc.date.available | 2023-03-21 19:03:04 (GMT) | |
dc.date.issued | 2018 | |
dc.identifier.uri | https://doi.org/10.1090/mcom/3231 | |
dc.identifier.uri | http://hdl.handle.net/10012/19220 | |
dc.description.abstract | We give algorithms for the evaluation of sparse polynomials of the form P=p0 + p1 x + p2 x^4 + ... + p_{n-1} x^{(N-1)^2} for various choices of coefficients . First, we take p_i=p^i, for some fixed p; in this case, we address the question of fast evaluation at a given point in the base ring, and we obtain a cost quasi-linear in sqrt{N}. We present experimental results that show the good behavior of this algorithm in a floating-point context, for the computation of Jacobi theta functions. Next, we consider the case of arbitrary coefficients; for this problem, we study the question of multiple evaluation: we show that one can evaluate such a polynomial at N values in the base ring in subquadratic time. | en |
dc.language.iso | en | en |
dc.publisher | American Mathematical Society | en |
dc.relation.ispartofseries | Mathematics of Computatation; | |
dc.subject | sparse polynomials | en |
dc.subject | evaluation | en |
dc.title | On the evaluation of some sparse polynomials | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Nogneng, D., & Schost, É. (2017). On the evaluation of some sparse polynomials. Mathematics of Computation, 87(310), 893–904. https://doi.org/10.1090/mcom/3231 | en |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.contributor.affiliation2 | David R. Cheriton School of Computer Science | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Reviewed | en |
uws.scholarLevel | Faculty | en |