03711nam 22006495 450 991031194040332120220415194039.03-030-04306-110.1007/978-3-030-04306-3(CKB)4100000007598457(DE-He213)978-3-030-04306-3(MiAaPQ)EBC5675627(PPN)235004340(EXLCZ)99410000000759845720190205d2018 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierNumerical Fourier analysis /by Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche1st ed. 2018.Cham :Springer International Publishing :Imprint: Birkhäuser,2018.1 online resource (XVI, 618 p. 51 illus., 30 illus. in color.)Applied and Numerical Harmonic Analysis,2296-50093-030-04305-3 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.Applied and Numerical Harmonic Analysis,2296-5009Harmonic analysisNumerical analysisInformation theoryMatrix theoryAlgebraAbstract Harmonic Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12015Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Information and Communication, Circuitshttps://scigraph.springernature.com/ontologies/product-market-codes/M13038Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Harmonic analysis.Numerical analysis.Information theory.Matrix theory.Algebra.Abstract Harmonic Analysis.Numerical Analysis.Information and Communication, Circuits.Linear and Multilinear Algebras, Matrix Theory.515.785515.2433Plonka Gerlindauthttp://id.loc.gov/vocabulary/relators/aut955746Potts Danielauthttp://id.loc.gov/vocabulary/relators/autSteidl Gabrieleauthttp://id.loc.gov/vocabulary/relators/autTasche Manfredauthttp://id.loc.gov/vocabulary/relators/autBOOK9910311940403321Numerical Fourier Analysis2163213UNINA