On Euler-Maclaurin formula

被引：2

作者：

Dubeau, Francois ^{[1
]}

机构：

[1] Univ Sherbrooke, Fac Sci, Dept Math, Sherbrooke, PQ J1K 2R1, Canada

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 296卷

关键词：

Euler-Maclaurin formula; Corrected quadrature rule; Composite rule; Taylor's expansion; Peano Kernel; Optimal error bounds;

D O I：

10.1016/j.cam.2015.10.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use a simple approach to show that an Euler-Maclaurin like formula can be associated to any interpolatory quadrature rule. This result is obtained by successively adding correcting terms that are exact for polynomials of increasing degree. A decomposition of the coefficients of the Euler Maclaurin formula in terms of the integral to compute and representations of powers of the nodes is pointed out. Optimal truncation error bounds are also obtained. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：649 / 660

页数：12

共 13 条

[1]

Adams R.A., 1975, Sobolev Spaces

[2]

ALALAOUI MA, 1996, ACM SIGNUM NEWSLETT, V31, P25, DOI DOI 10.1145/230922.230930

[3]

[Anonymous], 1966, 1 COURSE INTEGRATION

[4]

[Anonymous], 1948, Handbook of Mathematical Functions withFormulas, Graphs, and Mathematical Tables, DOI DOI 10.1119/1.15378

[5]

[Anonymous], 1950, Interpolation

[6] Euler-Boole Summation Revisited [J].

Borwein, Jonathan M. ;

Calkin, Neil J. ;

Manna, Dante .

AMERICAN MATHEMATICAL MONTHLY, 2009, 116 (05) :387-412

[7]

Brendt B., 1975, J NUMBER THEORY, V7, P413

[8]

Davis P.J., 1975, Methods of Numerical Integration

[9]

Dubeau F, 2014, J MATH ANAL, V5, P1

[10]

Lukas S.K., EULER MACLAURI UNPUB, P11

← 1 2 →