A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates

Gerard Gómez; Josep Maria Mondelo; Carles Simó

doi:10.3934/dcdsb.2010.14.75

A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates

Gerard Gómez, Josep Maria Mondelo, Carles Simó

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

14 Citations (Scopus)

Abstract

In a previous paper [6], a numerical procedure for the Fourier analysis of quasi-periodic functions was developed, allowing for an accurate determination of frequencies and amplitudes from equally-spaced samples of the input function on a finite time interval. This paper is devoted to a complete error analysis of that procedure, from which computable bounds are deduced. These bounds are verified and further discussed in examples.

Original language	English
Pages (from-to)	75-109
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	14
Issue number	1
DOIs	https://doi.org/10.3934/dcdsb.2010.14.75
Publication status	Published - 1 Jul 2010

Keywords

Fast fourier transform
Numerical fourier analysis
Quasi-periodic functions

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abstract = "In a previous paper [6], a numerical procedure for the Fourier analysis of quasi-periodic functions was developed, allowing for an accurate determination of frequencies and amplitudes from equally-spaced samples of the input function on a finite time interval. This paper is devoted to a complete error analysis of that procedure, from which computable bounds are deduced. These bounds are verified and further discussed in examples.",

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AU - Simó, Carles

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AB - In a previous paper [6], a numerical procedure for the Fourier analysis of quasi-periodic functions was developed, allowing for an accurate determination of frequencies and amplitudes from equally-spaced samples of the input function on a finite time interval. This paper is devoted to a complete error analysis of that procedure, from which computable bounds are deduced. These bounds are verified and further discussed in examples.

KW - Fast fourier transform

KW - Numerical fourier analysis

KW - Quasi-periodic functions

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DO - 10.3934/dcdsb.2010.14.75

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JO - Discrete and Continuous Dynamical Systems - Series B

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