Module and vector space bases for spline spaces
type: Item
instance of: scholarly article
title: Module and vector space bases for spline spaces
zbMATH Open document ID: 0732.41014
DOI: 10.1016/0021-9045(91)90113-O
author: Ruth Haas
published in: Journal of Approximation Theory
publication date: 1991-01-01T00:00:00Z
review text: One way of investigating the dimension of and bases for d-variate polynomial spline spaces \(S^ r_ m(\Delta)\) of given smoothness r and polynomial degree m is to view the union \(S^ r(\Delta)=\cup_{m}S^ r_ m(\Delta)\) as a module over the polynomial ring \({\mathbb{R}}[x_ 1,...,x_ d]\). In this paper, it is shown how in certain cases a module basis of \(S^ r(\Delta)\) can be used to find a vector space basis of \(S^ r_ m(\Delta)\) by establishing a relationship between the dimension of \(S^ r_ m(\Delta)\) and the degrees of reduced basis elements of \(S^ r(\Delta)\). Techniques for finding module bases are discussed, especially for cross-cut grids in \({\mathbb{R}}^ 2\).
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 4210754
zbMATH Keywords: polynomial spline spaces
reviewed by: E. Quak
MaRDI profile type: Publication
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full work available at URL: 0021-9045(91)90113-o
OpenAlex ID: W1986390133
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description: scientific article; zbMATH DE number 4210754