On multivariate Hermite interpolation
type: Item
instance of: scholarly article
title: On multivariate Hermite interpolation
zbMATH Open document ID: 0836.41004
DOI: 10.1007/BF03177515
author: Tomas Sauer
author: Yuan Xu
published in: Advances in Computational Mathematics
publication date: 1995-12-18T00:00:00Z
review text: The authors study the problem of Hermite interpolation by polynomials in several variables. They adopt a very general formulation of this problem, consisting in interpolation of consecutive chains of directional derivatives. By using the notion of blockwise structure introduced by the authors in a previous paper [Math. Comp. (to appear)], they establish an interpolation formula analogous to that of Newton in one variable and use it for obtaining an integral representation for the remainder. In order to illustrate the various definitions and results, numerous examples are presented throughout the paper.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 826883
zbMATH Keywords: remainder formula
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: blockwise structure
MaRDI profile type: Publication
cites work: General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
cites work: Q4095322
cites work: On multivariate polynomial interpolation
cites work: Computational Aspects of Polynomial Interpolation in Several Variables
cites work: On Lagrange and Hermite interpolation in \(R^ k\).
cites work: Multivariate Birkhoff interpolation
cites work: Computational aspects of multivariate polynomial interpolation
cites work: On Multivariate Lagrange Interpolation
full work available at URL: https://doi.org/10.1007/bf03177515
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description: scientific article; zbMATH DE number 826883