高斯正交公式是一类无限可微分函数的强渐近最优公式

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2024-10-24 DOI:10.1016/j.jat.2024.106117

Guiqiao Xu

引用次数: 0

摘要

本文研究了[-1,1]上一类无限微分函数 F∞ 的最优正交公式。我们得到了标准信息和赫米特数据下 F∞ 的最优最坏情况误差的强等价性。我们证明了高斯正交公式是强渐近最优的。

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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Gaussian quadrature formulae are strongly asymptotically optimal for a class of infinitely differentiable functions

This paper investigates the optimal quadrature formulae of a class

F_{\infty}

of infinitely differentiable functions on

[- 1, 1]

. We obtain the strong equivalences of the optimal worst case errors of

F_{\infty}

for standard information and Hermite data. We proved that the Gaussian quadrature formulae are strongly asymptotically optimal.

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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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