Expansion over a rectangle of real functions in Bernoulli polynomials and applications

被引：31

作者：

Costabile, FA ^{[1
]}

Dell'Accio, F ^{[1
]}

机构：

[1] Univ Calabria, Dipartmento Matemat, I-87036 Arcavacata Di Rende, CS, Italy

来源：

BIT | 2001年 / 41卷 / 03期

关键词：

Bernoulli polynomial; Taylor expansion; Sard kernels;

D O I：

10.1023/A:1021958910686

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper we generalize an expansion in Bernoulli polynomials for real functions possessing a sufficient number of derivatives. Starting from this expansion we obtain useful kernels, which are substantially different from Sard's for a wide class of linear functionals that includes the truncation error for cubature formulas.

引用

页码：451 / 464

页数：14

共 9 条

[1] An iterative method for the computation of the solutions of nonlinear equations [J].

Costabile, F ;

Gualtieri, MI ;

Capizzano, SS .

CALCOLO, 1999, 36 (01) :17-34

[2]

COSTABILE F, UNPUB EXPANSION SIMP

[3]

COSTABILE F, 1999, C SEM U BAR, V273

[4]

Davis P. J, 1975, Interpolation and Approximation

[5]

ENGELS H, 1990, NUMERICAL QUADRATURE

[6]

Jordan C., 1965, CALCULUS FINITE DIFF

[7]

SARD A, 1963, AM MATH SOC MATH SUR, V9

[8]

STANCU DD, 1964, SIAM J NUMER ANAL, V1, P137

[9]

Steffensen J.F, 1965, INTERPOLATION

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