Error estimates and convergence rates for variational Hermite interpolation
type: Item
instance of: scholarly article
title: Error estimates and convergence rates for variational Hermite interpolation
zbMATH Open document ID: 0915.41002
author: Zuhua Luo
author: Jeremy Levesley
published in: Journal of Approximation Theory
publication date: 1999-06-21T00:00:00Z
review text: Let \(E^{'}_r\) be a dual space to \(C^r(\mathbb R^d)\) and \(\Lambda=\{l_1,\dots,l_N\}\subseteq E_r^{'}\). The authors consider the \(h\)-spline Hermite interpolant \[ s(x)=\sum_{i=1}^N a_i*h(x)+\sum_{| j| <m}b_j x^j, \] satisfying \((L_i,s)=f_i\), \(1\leq i\leq n\), and \(\sum_{i=1}^{n}a_i(L_i,p)=0\) for polynomials \(p\) of degree less than \(m\). Assume that \(Y_j=\{y\in\mathbb R^d| D^j\sigma_y\in \Lambda\}\) and \(dist(Y_j,\omega)\leq \rho\). Then if \(M=D^k\delta_y\) for some \(k\in \mathbb Z^d\) such that \(| k| \leq r\), \(j\leq k\) and \(y\in\Omega\), we have \(| (M,f_s)| \leq C\rho^{r-| k| } \).
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1230424
zbMATH Keywords: Hermite interpolation
MaRDI profile type: Publication
OpenAlex ID: W1985891071
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DOI: 10.1006/JATH.1997.3218
description: scientific article; zbMATH DE number 1230424