Numerical Fourier Analysis

• Main Authors: Plonka, Gerlind (Author, 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)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Applied and Numerical Harmonic Analysis,
• Subjects: Harmonic analysis.; Numerical analysis.; Information theory.; Matrix theory.; Algebra.; Abstract Harmonic Analysis.; Numerical Analysis.; Information and Communication, Circuits.; Linear and Multilinear Algebras, Matrix Theory.
• Physical Description: XVI, 618 p. 51 illus., 30 illus. in color. online resource.
• ISBN: 9783030043063
• ISSN: 2296-5009
• DOI: 10.1007/978-3-030-04306-3

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.