論同時有理函數重構的唯一性（CS SC）

• 2020 年 3 月 27 日
• 筆記

本文給出了有理函數的一些估計，或者更一般地給出它們的餘子模不同多項式，重點討論了有理函數向量的重構問題。有理數共享相同分母的特殊情況，也被稱為：同步有理函數重構(Rational Function Reconstruction, SRFR)，它具有從線性系統求解到編碼理論的許多應用，只要SRFR具有唯一解。相對於有理函數的一般向量，SRFR中的未知數要少一些。這可以減少保證解決方案存在所需的評估點的數量，但是我們可能會失去它的唯一性。在本文中，我們證明了一個通用實例的唯一性是有保證的。

原文題目：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