Interpolation with symmetric polynomials
type: Item
instance of: scholarly article
title: Interpolation with symmetric polynomials
zbMATH Open document ID: 1357.41001
author: J. M. Carnicer
author: Carmen Godés
published in: Numerical Algorithms
publication date: 2017-01-12T00:00:00Z
review text: Interpolation problems in more than one dimensional ambient spaces are studied in this article. Whenever the dimension of the ambient space is more than one, these problems are a lot more difficult to analyse than the classical univariate problems, for instance because not only convergence properties but also existence questions of interpolants, dimensions of the underlying approximation spaces etc.\ now depend on the geometry of the data points. The current article addresses this fundamental problem by observing that certain symmetry properties facilitate the aforementioned problems substantially. They begin with studying even univariate symmetric (even and odd) polynomial interpolation problems (which provide the basis of the then ongoing approach for higher dimensions) and then continue by analysing symmetric (symmetric about a line in two dimensions) bivariate interpolation tasks, thereby reducing the problem substantially and concretely halving the dimension of the approximation space. The authors consider also more general interpolation problems by bringing them back to the previous shape already studied by decomposition into their symmetric and antisymmetric parts.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 6674007
zbMATH Keywords: bivariate polynomial interpolation
zbMATH Keywords: Lagrange interpolation
zbMATH Keywords: Berzolari-Radon sets
MaRDI profile type: Publication
full work available at URL: s11075-016-0135-6
OpenAlex ID: W2343188500
cites work: On polynomial interpolation of two variables
cites work: Interpolation on the disk
cites work: A Newton formula for generalized Berzolari-Radon sets
cites work: On Lattices Admitting Unique Lagrange Interpolations
cites work: On Lagrange and Hermite interpolation in \(R^ k\).
cites work: Interpolation systems in \(R^ k\)
cites work: Q3126966
cites work: Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle
cites work: Discrete Fourier analysis on a dodecahedron and a tetrahedron
cites work: Q3723033
cites work: Zur mechanischen Kubatur
cites work: Poised nodes set constructions on algebraic curves
DOI: 10.1007/S11075-016-0135-6
Recommended article: Interpolation by polynomials with symmetries
Recommended article: Interpolation for symmetric functions
Recommended article: Hermite interpolation with symmetric polynomials
Recommended article: Sparse interpolation of symmetric polynomials
Recommended article: Symmetric matrix polynomial equation: Interpolation results
Recommended article: Q4459974
Recommended article: Symmetrical formulas for rational interpolants
Recommended article: Interpolation and approximation by polynomials
description: scientific article; zbMATH DE number 6674007