论文标题
关于同时合理函数重建的独特性
On the Uniqueness of Simultaneous Rational Function Reconstruction
论文作者
论文摘要
本文重点是重建某些评估的理性函数向量的问题，或者更普遍地考虑其剩余的模型不同的多项式。共享相同分母的特殊情况，即又称合理函数重建（SRFR），只要SRFR具有独特的解决方案，就具有从线性系统求解到编码理论的许多应用程序。 SRFR中未知数的数量小于有理功能的一般向量。这允许减少保证解决方案存在所需的评估点的数量，但我们可能会失去其独特性。在这项工作中，我们证明了通用实例可以保证唯一性。
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.
