The upper bound for the Lebesgue constant for Lagrange interpolation in equally spaced points of the triangle

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2023-09-11 DOI:10.1016/j.jat.2023.105969

Natalia Baidakova

引用次数: 0

Abstract

An upper bound for the Lebesgue constant, i.e., the supremum norm of the operator of interpolation of a function in equally spaced points of a triangle by a polynomial of total degree less than or equal to $n$ is obtained. Earlier, the rate of increase of the Lebesgue constants with respect to $n$ for an arbitrary $d$ -dimensional simplex was established by the author. The upper bound proved in this article refines this result for $d = 2$ .

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三角形等距点拉格朗日插值Lebesgue常数的上界

得到了Lebesgue常数的上界，即用总次数小于或等于n的多项式在三角形的等距点上插值函数的算子的上确界范数。早些时候，作者建立了任意d维单纯形的勒贝格常数相对于n的增长率。本文中证明的上界对d=2的结果进行了改进。

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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