Some performances of local bivariate quadratic \(C^1\) quasi-interpolating splines on nonuniform type-2 triangulations
type: Item
instance of: scholarly article
title: Some performances of local bivariate quadratic \(C^1\) quasi-interpolating splines on nonuniform type-2 triangulations
zbMATH Open document ID: 1065.65012
author: Paola Lamberti
author: Catterina Dagnino
published in: Journal of Computational and Applied Mathematics
publication date: 2005-01-13T00:00:00Z
review text: The paper is concerned with spline approximations in two dimensions. Continuously differentiable quadratic B-splines are used as basis functions for an approximation by quasi-interpolation. The triangulations on which the B-splines are based are nonuniform and of type-2. The data points at which the approximated values are evaluated are mesh points in the support or close to the support of the B-splines, and there is a fixed number of them which are used. For this set-up, the approximated values orders are established which are nearly optimal. Also, the convergence is shown both for the approximand and for its partial derivatives. Finally, several numerical examples for the quasi-interpolants are presented.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 2127085
zbMATH Keywords: bivariate splines
zbMATH Keywords: approximation order by splines
zbMATH Keywords: quadratic B-splines
zbMATH Keywords: quasi-interpolation
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2004.02.017
OpenAlex ID: W2022518388
cites work: Monotonicity Preserving Surface Interpolation
cites work: Box splines
cites work: Q3728569
cites work: Q5185473
cites work: On the approximation power of bivariate quadratic \(C^1\) splines
cites work: Q4801522
cites work: Local spline approximation methods
cites work: Q4231173
cites work: Bivariate spline interpolation at grid points
cites work: Algorithm 792
cites work: Bernstein-Bézier methods for the construction of bivariate spline approximants
cites work: Q5290137
cites work: Q3895980
cites work: The dimension and basis of spaces of multivariate splines
cites work: Multivariate spline and its applications in science and technology
cites work: Q4225664
DOI: 10.1016/J.CAM.2004.02.017
description: scientific article; zbMATH DE number 2127085