An Algorithm for the Discretization of an Ideal Projector

JIANG Xue,ZHANG Shugong,LI Zhe

系统科学与复杂性(英文) ›› 2016, Vol. 29 ›› Issue (5) : 1400-1410.

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系统科学与复杂性(英文) ›› 2016, Vol. 29 ›› Issue (5) : 1400-1410. DOI: 10.1007/s11424-016-4114-8

An Algorithm for the Discretization of an Ideal Projector

    JIANG Xue1 , ZHANG Shugong1 , LI Zhe2
作者信息 +

An Algorithm for the Discretization of an Ideal Projector

    JIANG Xue1 , ZHANG Shugong1 , LI Zhe2
Author information +
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Abstract

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.

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JIANG Xue,ZHANG Shugong,LI Zhe. An Algorithm for the Discretization of an Ideal Projector. 系统科学与复杂性(英文), 2016, 29(5): 1400-1410 https://doi.org/10.1007/s11424-016-4114-8
JIANG Xue , ZHANG Shugong , LI Zhe. An Algorithm for the Discretization of an Ideal Projector. Journal of Systems Science and Complexity, 2016, 29(5): 1400-1410 https://doi.org/10.1007/s11424-016-4114-8
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