Fifty Years of Schoenberg's Problem on the Convergence of Spline Interpolation

被引：14

作者：

Volkov, Yu. S. ^{[1
,2
]}

Subbotin, Yu. N. ^{[3
,4
]}

机构：

[1] Russian Acad Sci, Siberian Branch, Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

[3] Russian Acad Sci, Inst Math & Mech, Ural Branch, Ekaterinburg 620990, Russia

[4] Ural Fed Univ, Inst Math & Comp Sci, Ekaterinburg 620000, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2015年 / 288卷

基金：

俄罗斯基础研究基金会;

关键词：

polynomial splines; interpolation; convergence; OPTIMAL ERROR-BOUNDS; L-INFINITY-BOUNDEDNESS; CUBIC-SPLINES; LEBESGUE CONSTANTS; 3RD DERIVATIVES; ODD-DEGREE; APPROXIMATION; METRICS; NORM;

D O I：

10.1134/S0081543815020236

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A review of results on the convergence of the interpolation process for polynomial splines and derivatives in the last 50 years is given.

引用

页码：S222 / S237

页数：16

共 112 条

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NILSON, EN
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AHLBERG, JH
NILSON, EN
WALSH, JL
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 54 (02) : 344 - &
[5] Ahlberg JH., 1967, THEORY SPLINES THEIR
[6] [Anonymous], 1968, TOTAL POSITIVITY
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Butzer, Paul L.
[J]. JOURNAL OF APPROXIMATION THEORY, 2009, 160 (1-2) : 3 - 18
[10] Cheney E. W., 1968, J APPROX THEORY, V1, P94

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