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Automated parameter tuning based on RMS errors for nonequispaced FFTs

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Abstract

In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the \(\mathcal {L}_{2}\)-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.

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Authors and Affiliations

  1. Faculty of Mathematics, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Franziska Nestler

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  1. Franziska Nestler
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Correspondence to Franziska Nestler.

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Communicated by: Leslie Greengard

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Nestler, F. Automated parameter tuning based on RMS errors for nonequispaced FFTs. Adv Comput Math 42, 889–919 (2016). https://doi.org/10.1007/s10444-015-9446-8

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  • DOI: https://doi.org/10.1007/s10444-015-9446-8

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