Approximation of 1/x by exponential sums in [1, ∞)

被引：91

作者：

Braess, D ^{[1
]}

Hackbusch, W

机构：

[1] Ruhr Univ Bochum, Inst Math, D-44780 Bochum, Germany

[2] Max Planck Inst Math Nat Wissensch, D-04103 Leipzig, Germany

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2005年 / 25卷 / 04期

关键词：

sums of exponentials; Chebyshev approximation;

D O I：

10.1093/imanum/dri015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Approximations of 1/x by sums of exponentials are well studied for finite intervals. Here the error decreases like O(exp(-ck)) with the order k of the exponential sum. In this paper we investigate approximations of 1/x in the interval [1, infinity). We prove estimates of the error by O(exp(-c root k)) and confirm this asymptotic estimate by numerical results. Numerical results lead to the conjecture that the constant in the exponent equals c = pi root 2.

引用

页码：685 / 697

页数：13

共 12 条

[1]

Borwein JM., 1987, PI AGM STUDY ANAL NU

[2] ASYMPTOTICS FOR THE APPROXIMATION OF WAVE-FUNCTIONS BY EXPONENTIAL-SUMS [J].