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＜電子ブック＞
Numerical Fourier Analysis / by Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
(Applied and Numerical Harmonic Analysis. ISSN:22965017)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2018
本文言語	英語
大きさ	XVI, 618 p. 51 illus., 30 illus. in color : online resource
著者標目	*Plonka, Gerlind author Potts, Daniel author Steidl, Gabriele author Tasche, Manfred author SpringerLink (Online service)
件　名	LCSH:Harmonic analysis LCSH:Numerical analysis LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Algebras, Linear FREE:Abstract Harmonic Analysis FREE:Numerical Analysis FREE:Mathematical Applications in Computer Science FREE:Linear Algebra
一般注記	Fourier series -- Fourier transforms -- Discrete Fourier transforms -- Multidimensional Fourier methods -- Fast Fourier transforms -- Chebyshev methods and fast DCT algorithms -- Fast Fourier transforms for nonequispaced data -- High dimensional FFT -- Numerical applications of DFT -- Prony method for reconstruction of structured functions This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms HTTP:URL=https://doi.org/10.1007/978-3-030-04306-3

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