Numerical Fourier Analysis (eBook, PDF) - Plonka, Gerlind; Potts, Daniel; Steidl, Gabriele; Tasche, Manfred
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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…mehr

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Produktbeschreibung
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.

Autorenporträt
¿Gerlind Plonka received the Ph.D. degree in mathematics and the Habilitation degree from the University of Rostock in 1993 and 1996, respectively. She was an Associate Professor of applied analysis at the University of Duisburg-Essen, Germany, from January 1998 to June 2010. Since July 2010, she works as a Full Professor of applied mathematics at the University of Göttingen, Germany. Her current research interests include numerical methods of Fourier analysis, wavelet theory, and inverse problems with applications to signal and image processing. Daniel Potts received his Ph.D. degree in mathematics from the University of Rostock in 1998. He held a research position at the University of Lübeck from 1996 to 2005, where he obtained his Habilitation degree in 2004. Since 2005 he works as a Full Professor at the TU Chemnitz. His research focuses on applied analysis, in particular computational harmonic analysis, and applications in scientific computing.  Gabriele Steidl received the Ph.D. degree in mathematics and the Habilitation degree from the University of Rostock in 1988 and 1991, respectively. She had positions as Associated Professor for mathematics at the TU Darmstadt and as Full Professor at the University of Mannheim and the TU Kaiserslautern, where she also worked as consultant of the Fraunhofer ITWM Kaiserslautern. Since 2020 she is Full Professor at the TU Berlin. In 2022 she became a SIAM Fellow. Her research interests include harmonic analysis, optimization, inverse problems and machine learning with applications in image and signal processing. Manfred Tasche received the Ph.D. degree in mathematics and the Habilitation degree from the University of Rostock in 1966 and 1976, respectively. He was Associate Professor and later Full Professor for Analysis and Numerical Mathematics at the University of Rostock from 1978 to 1993. Until 2008, he worked as substitute Professor and Assistant Professor at the University of Lübeck and the University of Rostock. Since 2008 he is retired. His research focuses on numerical analysis and approximation, Fourier analysis and applications in signal processing.