On the approximation order of splines on spherical triangulations
type: Item
instance of: scholarly article
title: On the approximation order of splines on spherical triangulations
zbMATH Open document ID: 1043.41007
author: Marian Neamtu
author: Larry L. Schumaker
published in: Advances in Computational Mathematics
publication date: 2004-05-27T00:00:00Z
review text: The standard splines on Euclidean spaces are piecewise algebraic polynomials on triangulations (in two dimensions) or on other partitions in higher dimensions. Polynomials on spheres which are suitable to approximation functions defined there are usually homogeneous polynomials, restricted to spheres. Additional smoothness conditions are added in all cases so that the splines are in \(C^r\), say. In this paper, approximations of this kind on spheres are carefully analysed with a special emphasis on their approximation (convergence) orders. Lower bounds on the approximation orders are provided where seminorms of the approximands appear in the bounds whose order is related to the polynomial degree of the spline.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 2069016
zbMATH Keywords: spherical splines
zbMATH Keywords: piecewise polynomial functions
zbMATH Keywords: spherical triangulations
zbMATH Keywords: Sobolev space
zbMATH Keywords: seminorm
zbMATH Keywords: approximation order
reviewed by: Martin D. Buhmann
MaRDI profile type: Publication
full work available at URL: b:acom.0000016430.93487.ec
OpenAlex ID: W1981387538
DOI: 10.1023/B:ACOM.0000016430.93487.EC
description: scientific article; zbMATH DE number 2069016