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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On primes in arithmetic progressions. Tsukuba journal of mathematics

  • H. Mikawa
  • Illinois J. Math
  • 2001
Highly Influential
5 Excerpts

Interpolation of shifted-lacunary polynomials

  • J. von zur Gathen, J. Gerhard
  • In Proc. Mathematical Aspects of Computer and…
  • 2003
Highly Influential
1 Excerpt

Hiroshi Mikawa , On primes in arithmetic progressions

  • J. Barkley Rosser, Lowell Schoenfeld
  • Tsukuba journal of mathematics
  • 2005

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