A unique multivariate Hermite interpolant on the simplex
type: Item
instance of: scholarly article
title: A unique multivariate Hermite interpolant on the simplex
zbMATH Open document ID: 0823.65011
DOI: 10.1016/S0022-247X(85)71122-5
author: Thomas F. Sturm
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-06-19T00:00:00Z
review text: The author constructs a polynomial which interpolates given function values and derivatives at the vertices of a regular \(N\)-simplex. The interpolant is written as a linear combination of basis polynomials which are all generated from a basis polynomial defined on the standard simplex. The approximant interpolates quadratic polynomials exactly and has the lowest possible degree. Under these conditions, the interpolant is unique and the lowest possible degree turns out to be 3. Such interpolants are useful in optimization methods. There exist \(O(n^ 3)\) methods to evaluate function values, gradient and Hessian matrix at a given point.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 765151
zbMATH Keywords: multivariate approximation
zbMATH Keywords: polynomial interpolation
zbMATH Keywords: optimization methods
MaRDI profile type: Publication
full work available at URL: s0022-247x(85)71122-5
OpenAlex ID: W3143272169
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description: scientific article; zbMATH DE number 765151