An algorithm for the discretization of an ideal projector |
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Authors: | Xue Jiang Shugong Zhang Zhe Li |
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Institution: | 1.Institute of Mathematics, Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education),Jilin University,Changchun,China;2.Department of Applied Mathematics, School of Science,Changchun University of Science and Technology,Changchun,China |
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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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