Bivariate splines on Tohǎneanu partition
type: Item
instance of: scholarly article
title: Bivariate splines on Tohǎneanu partition
zbMATH Open document ID: 1439.41006
author: Tatyana Sorokina
published in: Journal of Approximation Theory
publication date: 2018-06-06T00:00:00Z
review text: The author considers piecewise polynomials (splines) on triangulations of two-dimensional real spaces. Unlike the univariate splines, there are spline spaces with different dimensions in this situation, depending on the geometry of the triangulation of the set on which the splines are defined. The author considers bivariate splines on certain partitions, with smoothness \(r\) and degree \(2r\), that span spaces of higher dimension than the lower bounds found by Schumaker. The properties of the piecewise polynomials depend on a phenomenon called supersmoothness which means a higher smoothness than expected across interior edges of the triangulation. In the article, not only the mentioned splines are considered but it is shown in which way the dimension of the spline spaces is a result of the supersmoothness.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 6881301
zbMATH Keywords: bivariate splines
zbMATH Keywords: Bernstein-Bézier form
zbMATH Keywords: supersmoothness
zbMATH Keywords: dimension
MaRDI profile type: Publication
full work available at URL: j.jat.2018.04.004
OpenAlex ID: W2802050392
cites work: Spline Functions on Triangulations
cites work: From spline approximation to Roth's equation and Schur functors
cites work: Q3910883
cites work: Redundancy of smoothness conditions and supersmoothness of bivariate splines
cites work: Smooth planar \(r\)-splines of degree 2\(r\)
cites work: Multivariate spline space over cross-cut partition
DOI: 10.1016/J.JAT.2018.04.004
description: scientific article; zbMATH DE number 6881301