中文摘要：

理想的插值是 univariate Hermite 插值的归纳。每 univariate Hermite interpolant 是某 Lagrange interpolants 的 pointwise 限制，是众所周知的。然而，一个反例由谢克赫特曼·鲍里斯表演规定为超过二个变量，在那里存在不是任何 Lagrange interpolants 的限制的理想的 interpolants。考虑因此是自然的：给理想的 interpolant，怎么发现 Lagrange interpolants 的一个序列(如果任何) 收敛到它。作者为理想的插值把这个问题称为 discretization。这份报纸论述一个算法解决 discretization 问题。如果算法回来真，作者得到一套 pairwise 不同的点以便相应 Lagrange interpolants 收敛到给定的理想的 interpolant。

英文摘要：

Ideal interpolation is a generalization of the univariate Hermite interpolation. It is well known that every univariate Hermite interpolant is a pointwise limit of some Lagrange interpolants. However, a counterexample provided by Shekhtman Boris shows that, for more than two variables, there exist ideal interpolants that are not the limit of any Lagrange interpolants. So it is natural to consider： Given an ideal interpolant, how to find a sequence of Lagrange interpolants （if any） that converge to it. The authors call this problem the discretization for ideal interpolation. This paper presents an algorithm to solve the discretization problem. If the algorithm returns ＂True＂, the authors get a set of pairwise distinct points such that the corresponding Lagrange interpolants converge to the given ideal interpolant.