Estimates of Lebesgue constants for Lagrange interpolation processes by rational functions under mild restrictions to their fixed poles

被引：0

作者：

Kalmykov, Sergei ^{[1
,2
]}

Lukashov, Alexey ^{[3
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Math Sci, CMA Shanghai, Shanghai, Peoples R China

[2] Keldysh Inst Appl Math, Moscow 125047, Russia

[3] Natl Res Univ, Moscow Inst Phys & Technol, Moscow, Russia

来源：

JOURNAL OF APPROXIMATION THEORY | 2023年 / 291卷

关键词：

Interpolation; Lebesgue constant; Inverse polynomial images; Chebyshev-Markov fractions;

D O I：

10.1016/j.jat.2023.105909

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We estimate the Lebesgue constants for Lagrange interpolation processes on one or several intervals by rational functions with fixed poles. We admit that the poles have finitely many accumulation points on the intervals. To prove it we use an analog of the inverse polynomial image method for rational functions with fixed poles. (c) 2023 Elsevier Inc. All rights reserved.

引用

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页数：15

共 4 条

[1] Lebesgue Constants for Rational Interpolation Processes and Inverse Rational Functions Mappings
Kalmykov, Sergei
Lukashov, Alexey
INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020), 2021, 2325
[2] CONVEX FUNCTION APPROXIMATION BY INTERPOLATION RATIONAL FUNCTIONS WITH A FIXED NUMBER OF POLES
ROVBA, EA
DOKLADY AKADEMII NAUK BELARUSI, 1977, 21 (09): : 781 - 783
[3] On cardinal interpolation by Gaussian radial-basis functions: Properties of fundamental functions and estimates for Lebesgue constants
Riemenschneider, SD
Sivakumar, N
JOURNAL D ANALYSE MATHEMATIQUE, 1999, 79 (1): : 33 - 61
[4] On cardinal interpolation by Gaussian radial-basis functions: Properties of fundamental functions and estimates for Lebesgue constants
S. D. Riemenschneider
N. Sivakumar
Journal d’Analyse Mathématique, 1999, 79 : 33 - 61

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