Preprint 75/2004

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
MSC-Numbers: 11L07, 41A50
Keywords and phrases: exponential sums, approximation of functions
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Approximations of 1/x by sums of exponentials are well studied for finite intervals. Here the error decreases like formula13 with the order k of the exponential sum. In this paper we investigate approximations of 1/x on the interval formula19. We prove estimates of the error by formula21 and confirm this asymptotic estimate by numerical results. Numerical results lead to the conjecture that the constant in the exponent equals formula23

03.07.2017, 01:41