Lower bound for the Lebesgue function of an interpolation process with algebraic polynomials on equidistant nodes of a simplex

被引：0

作者：

Baidakova, N. V. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Inst Math & Mech, Ural Branch, Ekaterinburg, Russia

[2] Ural Fed Univ, Ekaterinburg, Russia

来源：

MATHEMATICAL NOTES | 2012年 / 92卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

interpolation process; equidistant nodes; algebraic polynomial; Lebesgue function; m-simplex; Lebesgue constant;

D O I：

10.1134/S0001434612070024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an interpolation process with algebraic polynomials of degree n on equidistant nodes of an m-simplex for m a parts per thousand yen 2, we obtain a pointwise lower bound for the Lebesgue function similar to the well-known estimate for interpolation on a closed interval.

引用

页码：16 / 22

页数：7

共 28 条

[1] Lower bound for the Lebesgue function of an interpolation process with algebraic polynomials on equidistant nodes of a simplex
N. V. Baidakova
Mathematical Notes, 2012, 92 : 16 - 22
[2] ON THE LEBESGUE FUNCTION FOR LAGRANGE INTERPOLATION WITH EQUIDISTANT NODES
MILLS, TM
SMITH, SJ
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1992, 52 : 111 - 118
[3] On the Order of the Lebesgue Constants for Interpolation by Algebraic Polynomials from Values at Uniform Nodes of a Simplex
N. V. Baidakova
Mathematical Notes, 2005, 77 : 751 - 766
[4] On the order of the lebesgue constants for interpolation by algebraic polynomials from values at uniform nodes of a simplex
Baidakova, NV
MATHEMATICAL NOTES, 2005, 77 (5-6) : 751 - 766
[5] INTERPOLATION POLYNOMIALS ON EQUIDISTANT NODES
MILLS, TM
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (02): : A279 - A279
[6] LEBESGUE CONSTANT FOR LAGRANGE INTERPOLATION ON EQUIDISTANT NODES
A. Eisinberg
G. Fedele
G. Franzè
AnalysisinTheoryandApplications, 2004, (04) : 323 - 331
[7] THE LEBESGUE CONSTANT FOR LAGRANGE INTERPOLATION ON EQUIDISTANT NODES
MILLS, TM
SMITH, SJ
NUMERISCHE MATHEMATIK, 1992, 61 (01) : 111 - 115
[8] On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
Bos, Len
De Marchi, Stefano
Hormann, Kai
Klein, Georges
NUMERISCHE MATHEMATIK, 2012, 121 (03) : 461 - 471
[9] On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
Len Bos
Stefano De Marchi
Kai Hormann
Georges Klein
Numerische Mathematik, 2012, 121 : 461 - 471
[10] Asymptotic behaviour of the Lebesgue constants of periodic interpolation splines with equidistant nodes
Subbotin, YN
Telyakovskii, SA
SBORNIK MATHEMATICS, 2000, 191 (7-8) : 1233 - 1242

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