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Analytic Continuation by the Fast Fourier Transform

Franklin, Joel (1990) Analytic Continuation by the Fast Fourier Transform. SIAM Journal of Scientific and Statistical Computing, 11 (1). pp. 112-122. ISSN 0196-5204. http://resolver.caltech.edu/CaltechAUTHORS:FRAsiamjssc90

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Abstract

The ill-posed problem of analytic continuation is regularized by a prescribed bound. A simple computer algorithm is given that is based on the fast Fourier transform. The algorithm computes $m$ complex values and a positive error bound with time complexity $O(m\log m)$. As a function of the data errors and the prescribed bound, the numerical error is shown to be consistent with that prescribed by the three-circles principle of Hadamard.


Item Type:Article
Additional Information:©1990 Society for Industrial and Applied Mathematics Received by the editors November 2, 1987; accepted for publication (in revised form) January 24, 1989.
Subject Keywords:analytic continuation, fast Fourier transform, ill posed
Record Number:CaltechAUTHORS:FRAsiamjssc90
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:FRAsiamjssc90
Alternative URL:http://dx.doi.org/10.1137/0911007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4869
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:11 Sep 2006
Last Modified:26 Dec 2012 09:02

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