It is well-known that the Floater-Hormann rational interpolants give better results than other rational interpolants, especially in convergence rates and barycentric form. In this paper, we propose and study a family of bivariate Floater-Hormann rational interpolants, which have no real poles and arbitrarily high convergence rates on any rectangular region. Moreover, these interpolants are linear on data. In the end, several numerical examples further confirm our results.

中文翻译：

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二元Floater-Hormann有理插值的一个收敛族

众所周知，Floater-Hormann有理插值比其他有理插值提供更好的结果，尤其是在收敛速度和重心形式上。在本文中，我们提出并研究了一个双变量Floater-Hormann有理插值族，它们在任何矩形区域上都没有实极，并且收敛速度任意高。而且，这些插值在数据上是线性的。最后，几个数值例子进一步证实了我们的结果。