Fast Multipoint-Evaluation of Bivariate Polynomials

Details Fast Multipoint-Evaluation of Bivariate Polynomials Fast Multipoint-Evaluation of Bivariate Polynomials

2004-03-12

arxiv.org/abs/cs/0403022v2

Computer Science

Data Structures and Algorithms

12 pages, 1 figure. To appear in Proc. 12th ESA 2004

Scientific paper

We generalize univariate multipoint evaluation of polynomials of degree n at sublinear amortized cost per point. More precisely, it is shown how to evaluate a bivariate polynomial p of maximum degree less than n, specified by its n^2 coefficients, simultaneously at n^2 given points using a total of O(n^{2.667}) arithmetic operations. In terms of the input size N being quadratic in n, this amounts to an amortized cost of O(N^{0.334}) per point.

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