LEADER 05016nam 22008175 450 001 9910760263003321 005 20240626154906.0 010 $a3-031-35005-7 024 7 $a10.1007/978-3-031-35005-4 035 $a(MiAaPQ)EBC30876562 035 $a(Au-PeEL)EBL30876562 035 $a(DE-He213)978-3-031-35005-4 035 $a(CKB)28804791400041 035 $a(EXLCZ)9928804791400041 100 $a20231108d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical Fourier Analysis /$fby Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (676 pages) 225 1 $aApplied and Numerical Harmonic Analysis,$x2296-5017 311 08$aPrint version: Plonka, Gerlind Numerical Fourier Analysis Cham : Springer International Publishing AG,c2023 9783031350047 327 $aChapter. 1. Fourier series -- Chapter. 2. Fourier transform -- Chapter. 3. Discrete Fourier transforms -- Chapter. 4. Multidimensional Fourier methods -- Chapter. 5. Fast Fourier transforms -- Chapter. 6. Chebyshev methods and fast DCT algorithms -- Chapter. 7. Fast Fourier transforms for nonequispaced data -- Chapter. 8. High dimensional FFT -- Chapter. 9. Numerical applications of DFT -- Chapter. 10. Prony method for reconstruction of structured functions -- Appendix A -- Index -- References. 330 $aNew technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications. 410 0$aApplied and Numerical Harmonic Analysis,$x2296-5017 606 $aFourier analysis 606 $aHarmonic analysis 606 $aNumerical analysis 606 $aComputer science$xMathematics 606 $aAlgebras, Linear 606 $aFourier Analysis 606 $aAbstract Harmonic Analysis 606 $aNumerical Analysis 606 $aMathematical Applications in Computer Science 606 $aLinear Algebra 606 $aAnàlisi de Fourier$2thub 606 $aAnàlisi harmònica$2thub 606 $aAnàlisi numèrica$2thub 606 $aÀlgebra lineal$2thub 608 $aLlibres electrònics$2thub 615 0$aFourier analysis. 615 0$aHarmonic analysis. 615 0$aNumerical analysis. 615 0$aComputer science$xMathematics. 615 0$aAlgebras, Linear. 615 14$aFourier Analysis. 615 24$aAbstract Harmonic Analysis. 615 24$aNumerical Analysis. 615 24$aMathematical Applications in Computer Science. 615 24$aLinear Algebra. 615 7$aAnàlisi de Fourier 615 7$aAnàlisi harmònica 615 7$aAnàlisi numèrica 615 7$aÀlgebra lineal 676 $a515.2433 676 $a515.2433 700 $aPlonka$b Gerlind$0955746 701 $aPotts$b Daniel$01438730 701 $aSteidl$b Gabriele$01438731 701 $aTasche$b Manfred$054571 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910760263003321 996 $aNumerical Fourier Analysis$93600365 997 $aUNINA