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Available4.5
6 reviewsMain subject categories: • Fourier Analysis • Numerical Analysis • Fourier Analysis ‒ Applications • Numerical Analysis ‒ Applications
Mathematics Subject Classification (2010): • 42-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces • 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis • 42A10 Trigonometric approximation • 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series • 42A20 Convergence and absolute convergence of Fourier and trigonometric series • 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type • 42A85 Convolution, factorization for one variable harmonic analysis • 42B05 Fourier series and coefficients in several variables • 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type • 42C15 General harmonic expansions, frames • 65B05 Extrapolation to the limit, deferred corrections • 65D15 Algorithms for approximation of functions • 65D32 Numerical quadrature and cubature formulas • 65F35 Numerical computation of matrix norms, conditioning, scaling • 65G50 Roundoff error …
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.
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