Dyadic Hermite interpolation on a rectangular mesh
type: Item
instance of: scholarly article
title: Dyadic Hermite interpolation on a rectangular mesh
zbMATH Open document ID: 0934.65009
DOI: 10.1023/A:1018943002601
author: Serge Dubuc
author: Jean-Louis Merrien
published in: Advances in Computational Mathematics
publication date: 2000-04-03T00:00:00Z
review text: The univariate bisection algorithm of the second author [Numer. Algorithms 2, 187 (1992; Zbl 0754.65011)] is extended to two variables. Assume that the values of a function \(f\) and its first derivatives \(p=f_x\) and \(q= f_y\) are given at the vertices of a rectangle \(R=I\times J\). The authors study a formula (depending on five parameters) which calculates from these data, values of \(f,p,q\) at the midpoint of \(R\) and at the midpoints of all edges of \(R\). This formula gives by iteration values for \(f,p,q\) at all dyadic points in \(R\). The question arises, of when this densely defined function can be extended to a \(C^1\) function on \(R\). A matrix representation of the interpolation formula and estimates for spectral radii are used to derive conditions on the parameters for which such a \(C^1\) extension is possible for all Hermite data. Several examples illustrate how the interpolation works for different sets of parameters.
reviewed by: Rudolf Wegmann
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1309408
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: numerical examples
zbMATH Keywords: bisectionalgorithm
MaRDI profile type: Publication
full work available at URL: a:1018943002601
OpenAlex ID: W2210085243
description: scientific article; zbMATH DE number 1309408