# Interpolation of Shifted-Lacunary Polynomials

@article{Giesbrecht2010InterpolationOS,
title={Interpolation of Shifted-Lacunary Polynomials},
author={Mark Giesbrecht and Daniel S. Roche},
journal={computational complexity},
year={2010},
volume={19},
pages={333-354}
}
Given a “black box” function to evaluate an unknown rational polynomial $$f \in {\mathbb{Q}}[x]$$ at points modulo a prime p, we exhibit algorithms to compute the representation of the polynomial in the sparsest shifted power basis. That is, we determine the sparsity $$t \in {\mathbb{Z}}_{>0}$$ , the shift $$\alpha \in {\mathbb{Q}}$$ , the exponents $${0 \leq e_{1} < e_{2} < \cdots < e_{t}}$$ , and the coefficients $$c_{1}, \ldots , c_{t} \in {\mathbb{Q}} \setminus \{0\}$$ such that f(x) = c_… CONTINUE READING
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