论同时有理函数重构的唯一性（CS SC）

• 2020 年 3 月 27 日
• 筆記

本文给出了有理函数的一些估计，或者更一般地给出它们的余子模不同多项式，重点讨论了有理函数向量的重构问题。有理数共享相同分母的特殊情况，也被称为：同步有理函数重构(Rational Function Reconstruction, SRFR)，它具有从线性系统求解到编码理论的许多应用，只要SRFR具有唯一解。相对于有理函数的一般向量，SRFR中的未知数要少一些。这可以减少保证解决方案存在所需的评估点的数量，但是我们可能会失去它的唯一性。在本文中，我们证明了一个通用实例的唯一性是有保证的。

原文题目：On the Uniqueness of Simultaneous Rational Function Reconstruction

原文：This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same denominator, a.k.a.Simultaneous Rational Function Reconstruction (SRFR), has many applications from linear system solving to coding theory, provided that SRFR has a unique solution. The number of unknowns in SRFR is smaller than for a general vector of rational function. This allows to reduce the number of evaluation points needed to guarantee the existence of a solution, but we may lose its uniqueness. In this work, we prove that uniqueness is guaranteed for a generic instance.

原文作者：Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore

原文地址：http://cn.arxiv.org/abs/2002.08748