# Query-efficient algorithms for polynomial interpolation over composites

@article{Gopalan2006QueryefficientAF,
title={Query-efficient algorithms for polynomial interpolation over composites},
author={Parikshit Gopalan},
journal={SIAM J. Comput.},
year={2006},
volume={38},
pages={1033-1057}
}
• P. Gopalan
• Published 22 January 2006
• Computer Science
• SIAM J. Comput.
The problem of polynomial interpolation is to reconstruct a polynomial based on its valuations on a set of inputs <i>I</i>. We consider the problem over <i>Z</i><inf>m</inf> when <i>m</i> is composite. We ask the question: Given I ⊆ <i>Z</i><inf>m</inf>, how many evaluations of a polynomial at points in I are required to compute its value at every point in I? Surprisingly for composite <i>m</i>, this number can vary exponentially between log[<i>I</i>] and [<i>I</i>] in contrast to the prime…
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