Approximation of 1∕x by Exponential Sums in [1,∞)

Dietrich Braess and Wolfgang Hackbusch

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Submission date: 28. Oct. 2004 (revised version: February 2005)
Pages: 14
published in: IMA journal of numerical analysis, 25 (2005) 4, p. 685-697 
DOI number (of the published article): 10.1093/imanum/dri015
Bibtex
MSC-Numbers: 11L07, 41A50
Keywords and phrases: exponential sums, approximation of functions
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Abstract:
Approximations of 1/x by sums of exponentials are well studied for finite intervals. Here the error decreases like with the order k of the exponential sum. In this paper we investigate approximations of 1/x on the interval . We prove estimates of the error by and confirm this asymptotic estimate by numerical results. Numerical results lead to the conjecture that the constant in the exponent equals