Multivariate polynomial splines on generalized oranges

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2024-01-15 DOI:10.1016/j.jat.2024.106016

Maritza Sirvent , Tatyana Sorokina , Nelly Villamizar , Beihui Yuan

引用次数: 0

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.

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广义桔子上的多变量多项式样条曲线

我们考虑的多元样条曲线空间定义在一种特殊的简单分区上，我们称之为（广义）桔子。这种分区由有限个最大面组成，其中有一个共享的中间面。我们把求桔子上的花键维数问题简化为计算更简单、更低维的分区上的花键维数，我们称之为投影桔子。我们同时使用代数和伯恩斯坦-贝塞尔工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.