Some identities for product and degree raising of splines
type: Item
instance of: scholarly article
title: Some identities for product and degree raising of splines
zbMATH Open document ID: 0732.41004
DOI: 10.1007/BF01888153
published in: Constructive Approximation
publication date: 1991-01-01T00:00:00Z
review text: It is shown how the algebraic product fg of two spline functions f and g, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. The author proves generalization of Marsden's identity and - based on this generalization - gives an explicit representation for the B-spline coefficients of a product of splines in terms of the B-spline coefficients of each factor. These results lead to simple generalizations of degree raising formulas of \textit{E. Cohen}, \textit{T. Lyche} and \textit{L. L. Schumaker} [J. Approximation Theory 46, 170-181 (1986; Zbl 0621.41009)].
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 4210745
zbMATH Keywords: B-splines
zbMATH Keywords: Marsden's identity
zbMATH Keywords: degree raising formulas
author: Knut Mørken
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01888153
OpenAlex ID: W2063872904
description: scientific article; zbMATH DE number 4210745