It is well-known that the Floater–Hormann interpolants give better results than other interpolants, especially in the case of equidistant points. In this paper, we generalize it to the Hermite case and establish a family of barycentric rational Hermite interpolants $r_m$ that do not suffer from divergence problems, unattainable points and occurrence of real poles. Furthermore, if the order $m$ of the Hermite interpolant is even and $f\in C^{(m+1)(d+1)+1+k}[a,b]$, the function $r_m^{\left(k\right)}$ converges to the corresponding function $f^{\left(k\right)}$ at the rate of $O\left(h^{(m+1)(d+1)-k}\right)$ as the mesh size $h\to 0$ for $k=0,1,2$, regardless of the distribution of the points; and if the interpolation points are quasi-equidistant and $f\in C^{(m+1)(d+1)+k}[a,b]$, the function $r_m^{\left(k\right)}$ converges to corresponding function $f^{\left(k\right)}$ at the rate of $O\left(h^{(m+1)(d+1)-1-2k}\right)$ as $h\to 0$ for $k=0,1,2$, regardless of the parity of the order $m$ of the Hermite interpolant.

众所周知，Floater-Hormann插值比其他插值提供更好的结果，尤其是在等距点的情况下。在本文中，我们将其推广到Hermite案例并建立一个重心有理Hermite插值族${\mathrm{[R}}_{米}$不会受到发散问题，无法达到的分数和实际极点的困扰。此外，如果订单$米$ Hermite插值的偶数和 $F\in C^{（米+\mathrm{1个}）（d+\mathrm{1个}）+\mathrm{1个}+ķ}[\mathrm{一种}，b]$， 功能 ${\mathrm{[R}}_{米}^{（ķ）}$ 收敛到相应的功能 $F^{（ķ）}$ 以...的速度 $Ø（H^{（米+\mathrm{1个}）（d+\mathrm{1个}）-ķ}）$ 作为网眼尺寸 $H\to 0$ 为了 $ķ=0，\mathrm{1个}，\mathrm{2个}$，无论积分的分布如何；并且如果插值点是准等距的，并且$F\in C^{（米+\mathrm{1个}）（d+\mathrm{1个}）+ķ}[\mathrm{一种}，b]$， 功能 ${\mathrm{[R}}_{米}^{（ķ）}$ 收敛到相应的功能 $F^{（ķ）}$ 以...的速度 $Ø（H^{（米+\mathrm{1个}）（d+\mathrm{1个}）-\mathrm{1个}-\mathrm{2个}ķ}）$ 作为 $H\to 0$ 为了 $ķ=0，\mathrm{1个}，\mathrm{2个}$，而不考虑订单的平价 $米$ Hermite插值器。