在本文中，Floater 和 Hormann 引入的插值有理函数被推广，产生了一个全新的有理函数族，具体取决于γ，一个附加的正整数参数。为了γ=1，获得原始的 Floater-Hormann 插值。什么时候γ>1我们证明新的有理函数具有原始 Floater-Hormann 函数的许多优良特性。事实上，对于紧凑区间中的任何节点配置，它们没有实极点，对给定数据进行插值，将多项式保留到一定的固定程度，并且具有重心型表示。此外，我们根据最小值（H*）和最大（H) 两个连续节点之间的距离。事实证明，与原始的 Floater-Hormann 插值相比，对于所有γ>1在等距和准等距节点配置的情况下（即，当H～H*）。对于这样的配置，随着节点数量趋于无穷大，我们证明新的插值（γ>1) 一致收敛于插值函数F，对于任何连续函数F和所有γ>1。原始 FH 插值不能保证同样的效果（γ=1）。此外，我们为具有不同平滑度的函数提供近似误差的统一和逐点估计。数值实验说明了理论结果，并显示了与原始 Floater-Hormann 插值相比，不太平滑的函数具有更好的误差曲线。

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In this paper the interpolating rational functions introduced by Floater and Hormann are generalized leading to a whole new family of rational functions depending on γ, an additional positive integer parameter. For γ=1, the original Floater–Hormann interpolants are obtained. When γ>1 we prove that the new rational functions share a lot of the nice properties of the original Floater–Hormann functions. Indeed, for any configuration of nodes in a compact interval, they have no real poles, interpolate the given data, preserve the polynomials up to a certain fixed degree, and have a barycentric-type representation. Moreover, we estimate the associated Lebesgue constants in terms of the minimum (h∗) and maximum (h) distance between two consecutive nodes. It turns out that, in contrast to the original Floater–Hormann interpolants, for all γ>1 we get uniformly bounded Lebesgue constants in the case of equidistant and quasi-equidistant nodes configurations (i.e., when h∼h∗). For such configurations, as the number of nodes tends to infinity, we prove that the new interpolants (γ>1) uniformly converge to the interpolated function f, for any continuous function f and all γ>1. The same is not ensured by the original FH interpolants (γ=1). Moreover, we provide uniform and pointwise estimates of the approximation error for functions having different degrees of smoothness. Numerical experiments illustrate the theoretical results and show a better error profile for less smooth functions compared to the original Floater–Hormann interpolants.