On the convergence rates of subdivision algorithms for box spline surfaces
type: Item
instance of: scholarly article
title: On the convergence rates of subdivision algorithms for box spline surfaces
zbMATH Open document ID: 0629.41008
DOI: 10.1007/BF01890038
author: B. George
published in: Constructive Approximation
publication date: 1985-01-01T00:00:00Z
review text: Let \({\mathfrak C}\) be the control net for some (parametric) spline surface \({\mathfrak S}\). Subdivision algorithms for generating \({\mathfrak S}\) are based on the idea of generating from \({\mathfrak C}\) the refined control net \({\mathfrak RC}\) such that \({\mathfrak RC}\) tends to \({\mathfrak S}\) as the level of refinement tends to zero. For the general setting of box splines the first author and \textit{C. A. Micchelli} [Comput. Aided Geom. Des. 1, 115- 129 (1984; Zbl 0581.65011)] have shown that \({\mathfrak RC}\) converges to \({\mathfrak S}\) at (at least) the rate of the refinement. In the paper under review some mild additional assumptions guaranteeing quadratic rate of convergence are established. Estimates for the convergence rate provide an adequate a priori choice of the level of the refinement of the control net.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 68U99
zbMATH DE Number: 4023935
zbMATH Keywords: box splines
zbMATH Keywords: Estimates
zbMATH Keywords: control net
MaRDI profile type: Publication
cites work: B-splines from parallelepipeds
cites work: Translates of multivariate splines
cites work: Q5185474
cites work: Subdivision algorithms for the generation of box spline surfaces
cites work: A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
cites work: Q3791625
Recommended article: Box splines revisited: Convergence and acceleration methods for the subdivision and the cascade algorithms
Recommended article: Subdivision algorithms for the generation of box spline surfaces
Recommended article: Deriving Box-Spline Subdivision Schemes
Recommended article: Interpolatory subdivision schemes induced by box splines
Recommended article: Q3034281
Recommended article: On the convergence of convolved vector subdivision schemes
Recommended article: Scalar multivariate subdivision schemes and box splines
Recommended article: Discrete box splines and refinement algorithms
Recommended article: Q3147722
Recommended article: On the convergence of multidimensional nonstationary subdivision schemes
description: scientific article; zbMATH DE number 4023935