使用小素数的并行稀疏插值

Mohamed Khochtali, Daniel S. Roche, Xisen Tian
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引用次数: 2

摘要

要插值具有整数系数的超稀疏多项式,有两种替代方法是基于prony的“大素数”技术,它作用于单个大有限域,或者最近提出的“小素数”技术,它将未知的稀疏多项式减少为许多低次密集多项式。虽然后一种技术尚未达到与基于prony的方法相同的理论效率,但它具有明显的并行化潜力。我们提出了一种启发式“小素数”插值算法,并报告了使用FLINT和MPI的低级C实现。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Parallel sparse interpolation using small primes
To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based "big prime" technique, which acts over a single large finite field, or the more recently-proposed "small primes" technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic "small primes" interpolation algorithm and report on a low-level C implementation using FLINT and MPI.
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