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Error Formulas for Ideal Interpolation

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arxiv 1506.05242 v3 pith:I4ZFLKC7 submitted 2015-06-17 math.NA cs.NA

Error Formulas for Ideal Interpolation

Yihe Gong , Xue Jiang , Zhe Li , Shugong Zhang This is my paper
classification math.NA cs.NA
keywords errorformulaformulasidealinterpolationexamplenormaladmits
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In this paper we study the algebraic structure of error formulas for ideal interpolation. We introduce the so-called "normal" error formulas and prove that the lexicographic order reduced Gr\"obner basis admits such a formula for all ideal interpolation. This formula is a generalization of the "good" error formula proposed by Carl de Boor. Finally, we discuss a Shekhtman's example and give an explicit form of "normal" error formula for this example.

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