An algorithm for the discretization of an ideal projector

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• 作者：Xue Jiang ; Shugong Zhang ; Zhe Li
• 关键词：Discretization ; ideal interpolation ; Lagrange interpolation
• 刊名：Journal of Systems Science and Complexity
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：29
• 期：5
• 页码：1400-1410
• 全文大小：205 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory and Control
  Applied Mathematics and Computational Methods of Engineering
  Operations Research/Decision Theory
  Probability Theory and Stochastic Processes
  
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences, co-published with Springer
• ISSN：1559-7067
• 卷排序：29

文摘

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.