Interpolation by Uni- and Multivariate Generalized Splines

Lagrange interpolation by finite-dimensional spaces of uni- and multivariate generalized spline functions (including polynomial splines) is studied. Using a condition of Schoenberg-Whitney type, it is shown how to change an almost interpolation set in order to obtain a set which admits unique Lagran...

Full description

Saved in:
Bibliographic Details
Published in:Journal of approximation theory 1995, Vol.83 (3), p.423-447
Main Authors: Sommer, M., Strauss, H.
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Lagrange interpolation by finite-dimensional spaces of uni- and multivariate generalized spline functions (including polynomial splines) is studied. Using a condition of Schoenberg-Whitney type, it is shown how to change an almost interpolation set in order to obtain a set which admits unique Lagrange interpolation. Moreover, it is shown that every regular space of univariate generalized splines is a weak Chebyshev space if and only if every interpolation set can be characterized by a modified Schoenberg-Whitney type condition.
ISSN:0021-9045
1096-0430
DOI:10.1006/jath.1995.1129