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Multivariate polynomial splines on generalized oranges

Maritza Sirvent, Tatyana Sorokina, Nelly Villamizar Orcid Logo, Beihui Yuan

Journal of Approximation Theory, Volume: 299, Start page: 106016

Swansea University Author: Nelly Villamizar Orcid Logo

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DOI (Published version): 10.1016/j.jat.2024.106016

Abstract

We consider spaces of multivariate splines defined on a particular type of simplicial partitions that we call (generalized) oranges. Such partitions are composed of a finite number of maximal faces with exactly one shared medial face. We reduce the problem of finding the dimension of splines on oran...

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Published in: Journal of Approximation Theory
ISSN: 0021-9045
Published: Elsevier BV 2024
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa65585
Abstract: We consider spaces of multivariate splines defined on a particular type of simplicial partitions that we call (generalized) oranges. Such partitions are composed of a finite number of maximal faces with exactly one shared medial face. We reduce the problem of finding the dimension of splines on oranges to computing dimensions of splines on simpler, lower-dimensional partitions that we call projected oranges. We use both algebraic and Bernstein–Bézier tools.
Keywords: Multivariate spline functions; Dimension of spline spaces; Bernstein–Bézier methods; Cofactor criterion
College: Faculty of Science and Engineering
Funders: EPSRC New Investigator Award EP/V012835/1
Start Page: 106016

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