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

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July 2010, 14(1): 75-109. 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 ^1, , Josep–Maria Mondelo ^2, and Carles Simó ^1,

1.	Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona
2.	Departament de Matemátiques, Universitat Autónoma de Barcelona, Edifici C, 08193 Bellaterra (Barcelona)

Received June 2009 Revised January 2010 Published April 2010

Abstract
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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.

Keywords: quasi-periodic functions., Numerical Fourier analysis, Fast Fourier Transform.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: Gerard Gómez, Josep–Maria Mondelo, Carles Simó. A collocation method for the numerical Fourier analysis of quasi-periodic functions. II: Analytical error estimates. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 75-109. doi: 10.3934/dcdsb.2010.14.75

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