We treat the interpolation problem ${\{f\left(x_j\right)=y_j\}}_{j=1}^N$ for polynomial and rational functions. Developing the approach originated by C. Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences of special symmetric functions of the data set like ${\{{\sum }_{j=1}^N{x}_j^k{y}_j/W^{\prime }\left(x_j\right)\}}_{k\in \mathbb{N}}$ and ${\{{\sum }_{j=1}^N{x}_j^k/\left(y_j{W}^{\prime }\left(x_j\right)\right)\}}_{k\in \mathbb{N}}$; here, $W\left(x\right)={\prod }_{j=1}^N(x-x_j)$. We also review the results by Jacobi, Joachimsthal, Kronecker and Frobenius on the recursive procedure for computation of the sequence of Hankel polynomials. The problem of evaluation of the resultant of polynomials $p\left(x\right)$ and $q\left(x\right)$ given a set of values ${\{p\left(x_j\right)/q\left(x_j\right)\}}_{j=1}^N$ is also tackled within the framework of this approach. An effective procedure is suggested for recomputation of rational interpolants in case of extension of the data set by an extra point.

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有理插值：雅可比方法回忆

我们处理插值问题 ${\{F\left(X_j\right)={是}_j\}}_{j=1}^N$对于多项式和有理函数。开发由 C. Jacobi 提出的方法，我们借助由数据集的特殊对称函数序列生成的 Hankel 多项式来表示插值，例如${\{{\sum }_{j=1}^N{X}_j^{克}{是}_j/{宽}^{\prime }\left(X_j\right)\}}_{克\in \mathbb{N}}$ 和 ${\{{\sum }_{j=1}^N{X}_j^{克}/\left({是}_j{宽}^{\prime }\left(X_j\right)\right)\}}_{克\in \mathbb{N}}$; 这里，$宽\left(X\right)={\prod }_{j=1}^N(X-X_j)$. 我们还回顾了 Jacobi、Joachimsthal、Kronecker 和 Frobenius 关于计算 Hankel 多项式序列的递归程序的结果。多项式结果的求值问题$磷\left(X\right)$ 和 $q\left(X\right)$ 给定一组值 ${\{磷\left(X_j\right)/q\left(X_j\right)\}}_{j=1}^N$也在这种方法的框架内处理。在数据集扩展了一个额外点的情况下，建议了一个有效的程序来重新计算有理插值。