Quasi-uniform designs with optimal and near-optimal uniformity constant

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2023-10-01 DOI:10.1016/j.jat.2023.105931

L. Pronzato , A. Zhigljavsky

引用次数: 1

Abstract

A design is a collection of distinct points in a given set $X$ , which is assumed to be a compact subset of $R^{d}$ , and the mesh-ratio of a design is the ratio of its fill distance to its separation radius. The uniformity constant of a sequence of nested designs is the smallest upper bound for the mesh-ratios of the designs. We derive a lower bound on this uniformity constant and show that a simple greedy construction achieves this lower bound. We then extend this scheme to allow more flexibility in the design construction.

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具有最优和近似最优均匀常数的拟均匀设计

设计是给定集合X中不同点的集合，该集合被假设为Rd的紧子集，设计的网格比率是其填充距离与其分离半径的比率。嵌套设计序列的均匀性常数是设计的网格比例的最小上界。我们推导了这个一致性常数的下界，并证明了一个简单的贪婪构造实现了这个下界。然后，我们对该方案进行了扩展，以便在设计和施工方面具有更大的灵活性。

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.

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