B 样条的对数凹性
IF 0.9
3区 数学
Q2 MATHEMATICS
引用次数: 0
摘要
库里和舍恩伯格通过将布鲁恩定理应用于单纯形，证明了 B-样条曲线在其支点上是对数凹的。在本论文中，我们仅使用 B-样条曲线及其一阶导数和二阶导数的递推公式，为对数凹性质提供了另一种 "解析 "证明。本文章由计算机程序翻译，如有差异，请以英文原文为准。
Log-concavity of B-splines
Curry and Schoenberg showed that a B-spline is log-concave in its support by applying Brunn’s theorem to a simplex. In this note we provide an alternative, ‘analytic’ proof of the log-concave property using only recursion formulas for B-splines and their first and second derivatives.
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来源期刊
CiteScore
1.90
自引率
11.10%
发文量
55
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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