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Journal Articles Journal of Complexity Year : 2021

Fast amortized multi-point evaluation

Joris van Der Hoeven
Grégoire Lecerf


The efficient evaluation of multivariate polynomials at many points is an important operation for polynomial system solving. Kedlaya and Umans have recently devised a theoretically efficient algorithm for this task when the coefficients are integers or when they lie in a finite field. In this paper, we assume that the set of points where we need to evaluate is fixed and "sufficiently generic". Under these restrictions, we present a quasi-optimal algorithm for multi-point evaluation over general fields. We also present a quasi-optimal algorithm for the opposite interpolation task.
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hal-02508529 , version 1 (14-03-2020)



Joris van Der Hoeven, Grégoire Lecerf. Fast amortized multi-point evaluation. Journal of Complexity, In press, ⟨10.1016/j.jco.2021.101574⟩. ⟨hal-02508529⟩
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