On dimension and existence of local bases for multivariate spline spaces

DOI10.1016/0021-9045(92)90087-5zbMath0761.41007OpenAlexW2071571965MaRDI QIDQ1198155

Peter Alfeld, Maritza Sirvent, Larry L. Schumaker

Publication date: 16 January 1993

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(92)90087-5

zbMATH Keywords

polynomial splinesBernstein-Bézier techniquestrivariate spline spaces

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Spline approximation (41A15)

Related Items

\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension, Recursive computation of bivariate Hermite spline interpolants, On multiresolution analysis of multiplicity \(d\), Multivariate $$C^1$$-Continuous Splines on the Alfeld Split of a Simplex, Lower Bound on the Dimension of Trivariate Splines on Cells, Lattice-supported splines on polytopal complexes, A lower bound for the dimension of tetrahedral splines in large degree, Multivariate polynomial splines on generalized oranges, Mini-workshop: Interpolation, approximation, and algebra. Abstracts from the mini-workshop held February 13--19, 2022, Bounds on the dimension of trivariate spline spaces: a homological approach, Optimal estimates for the linear interpolation error on simplices, Multivariate polynomial spline spaces, Dimension of \(C^1\)-splines on type-6 tetrahedral partitions, Stable local bases for multivariate spline spaces, A local Lagrange interpolation method based on $C^{1}$ cubic splines on Freudenthal partitions, The generic dimensions of the space of smooth splines of degree 7 on tetrahedral partitions, Developments in bivarite spline interpolation, Generalized integer splines on arbitrary graphs, Quasi-interpolation by quadratic piecewise polynomials in three variables

Cites Work

• Properties of \(n\)-dimensional triangulations
• A trivariate Clough-Tocher scheme for tetrahedral data
• Bounds on the dimension of spaces of multivariate piecewise polynomials
• The dimension of bivariate spline spaces of smoothness r for degree \(d\geq 4r+1\)
• Dual bases for spline spaces on cells
• Minimally supported bases for spaces of bivariate piecewise polynomials of smoothness r and degree \(d\geq 4r+1\)
• Super spline spaces of smoothness \(r\) and degree \(d\geq{} 3r+2\)
• Instability in the Dimension of Spaces of Bivariate Piecewise Polynomials of Degree $2r$ and Smoothness Order r
• The Condition of the B-Spline Basis for Polynomials
• An Explicit Basis for $C^1 $ Quartic Bivariate Splines
• A Nodal Basis for C 1 Piecewise Polynomials of Degree n ≥5
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item