Numerical Fourier Analysis

• Κύριοι συγγραφείς: Plonka, Gerlind (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Potts, Daniel (http://id.loc.gov/vocabulary/relators/aut), Steidl, Gabriele (http://id.loc.gov/vocabulary/relators/aut), Tasche, Manfred (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Applied and Numerical Harmonic Analysis,
• Θέματα: Harmonic analysis.; Numerical analysis.; Information theory.; Matrix theory.; Algebra.; Abstract Harmonic Analysis.; Numerical Analysis.; Information and Communication, Circuits.; Linear and Multilinear Algebras, Matrix Theory.

 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. 

 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.