Multivariate polynomial spline spaces
type: Item
instance of: scholarly article
title: Multivariate polynomial spline spaces
zbMATH Open document ID: 0952.65018
author: Yanyan Li
published in: Rocky Mountain Journal of Mathematics
publication date: 2001-01-02T00:00:00Z
full work available at URL: CONT29-3.html
review text: Spaces of polynomial splines are considered in \(p (\geq 2)\) variables, defined on rectangular grids. This paper provides a natural generalization of the bivariate case as studied by \textit{C. K. Chui} and \textit{R. H. Wang} [J. Math. Anal. Appl. 94, 197-221 (1983, Zbl 0526.41027)] to the \(p\)-variate case. The smoothness conditions imposed can be homogeneous, semi-homogeneous or nonhomogeneous [see \textit{C. K. Chui} and \textit{R. H. Wang}, Math. Comput. 41, 131-142 (1983, Zbl 0542.41008)]. Bases, and hence dimensions, for the polynomial spline spaces for these different smoothness cases are explicitly constructed. The bases can be written in terms of polynomials and truncated powers and products of these functions.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 1439635
zbMATH Keywords: multivariate splines
zbMATH Keywords: polynomial splines
MaRDI profile type: Publication
OpenAlex ID: W1964010372
cites work: On dimension and existence of local bases for multivariate spline spaces
cites work: Q3966560
cites work: Multivariate spline spaces
cites work: On Smooth Multivariate Spline Functions
cites work: A practical guide to splines
cites work: Q4731636
cites work: Q3346746
DOI: 10.1216/RMJM/1181071609
Recommended article: Multivariate splines and polytopes
Recommended article: Multivariate splines and polynomial interpolation
Recommended article: Q4713382
Recommended article: Q4731622
Recommended article: Special multivariate quadratic spline space
Recommended article: Multivariate splines and the Bernstein-Bézier form of a polynomial
Recommended article: Multivariate splines and hyperplane arrangements
Recommended article: Multivariate Spline Functions, B-Spline Basis and Polynomial Interpolations
Recommended article: Multivariate differences, polynomials, and splines
Recommended article: The dimension and basis of spaces of multivariate splines
description: scientific article; zbMATH DE number 1439635