THE GIBBS PHENOMENON FOR FOURIER INTERPOLATION

被引：29

作者：

HELMBERG, G

机构：

[1] Institut für Mathematik and Geometrik, Universität Innsbruck, A 6020 Innsbruck

来源：

JOURNAL OF APPROXIMATION THEORY | 1994年 / 78卷 / 01期

关键词：

D O I：

10.1006/jath.1994.1059

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Fourier interpolation polynomials for periodic functions with an isolated jump discontinuity exhibit for growing order a Gibbs phenomenon. The over- and undershots differ, however, from the ones appearing for the partial sums of the Fourier series and depend on the coincidence of the jump with interpolation nodes. (C) 1994 Academic Press, Inc.

引用

页码：41 / 63

页数：23

共 9 条

[1] Bojanic R., 1983, CANADIAN MATH SOC C, V3, P5
[2] DELAVALLEEPOUSS.CJ, 1908, B ACAD ROY BELGIQUE, P319
[3] THE GIBBS PHENOMENON FOR PIECEWISE-LINEAR APPROXIMATION
FOSTER, J
RICHARDS, FB
[J]. AMERICAN MATHEMATICAL MONTHLY, 1991, 98 (01) : 47 - 49
[4] HELMBERG G, 1991, GIBBS PHENOMENON FOU
[5] GIBBS-WILBRAHAM PHENOMENON - EPISODE IN FOURIER-ANALYSIS
HEWITT, E
HEWITT, RE
[J]. ARCHIVE FOR HISTORY OF EXACT SCIENCES, 1979, 21 (02) : 129 - 160
[6] RUNCK PO, 1962, J REINE ANGEW MATH, V210, P175
[7] Schwarz H.R., 1986, NUMERISCHE MATH
[8] Zygmund A, 1968, TRIGONOMETRIC SERIES, V2
[9] Zygmund A., 1968, TRIGONOMETRIC SERIES, VI

← 1 →