An algorithm for the discretization of an ideal projector
An algorithm for the discretization of an ideal projector
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DOI：
10.1007/s11424-016-4114-8
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发表时间：
2016-08
影响因子：
2.1
通讯作者：
Xue Jiang;Shugong Zhang;Zhe Li
中科院分区：
文献类型：
--
作者：
Xue Jiang;Shugong Zhang;Zhe Li
理想插值是一元Hermite插值的推广。众所周知，每一个一元Hermite插值都是某些拉格朗日插值的逐点极限。然而，Shekhtman Boris提供的一个反例表明，对于两个以上的变量，存在理想插值，它不是任何拉格朗日插值的极限。因此，很自然地要考虑：给定一个理想插值，如何找到收敛于它的一列拉格朗日插值（如果有的话），作者称这个问题为理想插值的离散化。本文提出了一种求解离散化问题的算法。如果算法返回“True”，则得到一组两两不同的点，使得相应的拉格朗日插值收敛于给定的理想插值。
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.