Multivariate polynomial interpolation on lower sets

Nira Dyn; Michael S. Floater

doi:10.1016/j.jat.2013.09.008

Multivariate polynomial interpolation on lower sets

Nira Dyn, Michael S. Floater^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Oslo

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

In this paper we study multivariate polynomial interpolation on lower sets of points. A lower set can be expressed as the union of blocks of points. We show that a natural interpolant on a lower set can be expressed as a linear combination of tensor-product interpolants over various intersections of the blocks that define it.

Original language	English
Pages (from-to)	34-42
Number of pages	9
Journal	Journal of Approximation Theory
Volume	177
DOIs	https://doi.org/10.1016/j.jat.2013.09.008
State	Published - Jan 2014

Keywords

Lower sets
Multivariate polynomial interpolation
Tensor-product interpolants

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10.1016/j.jat.2013.09.008

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title = "Multivariate polynomial interpolation on lower sets",

abstract = "In this paper we study multivariate polynomial interpolation on lower sets of points. A lower set can be expressed as the union of blocks of points. We show that a natural interpolant on a lower set can be expressed as a linear combination of tensor-product interpolants over various intersections of the blocks that define it.",

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AB - In this paper we study multivariate polynomial interpolation on lower sets of points. A lower set can be expressed as the union of blocks of points. We show that a natural interpolant on a lower set can be expressed as a linear combination of tensor-product interpolants over various intersections of the blocks that define it.

KW - Lower sets

KW - Multivariate polynomial interpolation

KW - Tensor-product interpolants

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JO - Journal of Approximation Theory

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Multivariate polynomial interpolation on lower sets

Abstract

Keywords

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