快速傅里葉變換的計算框架

內(nèi)容概要

the fast fourier transform (fft) family of
algorithms has revolutionized many areas of scientific computation.
the fft is one of the most widely used algorithms in science and
engineering, with applications in almost every discipline. this
volume is the most comprehensive treatment of ffts to date.
van loan captures the interplay between mathematics and the design
of effective numerical algorithms-a critical connection as more
advanced machines become available. he uses a stylized matlab
notation, which is familiar to those engaged in high-performance
computing.
this volume is essential for professionals interested in linear
algebra as well as those working with numerical methods. the fft is
also a great vehicle for teaching key aspects of scientific
computing.

作者簡介

Charles Van Loan has been with the department of computer
science at Cornell University since 1975 and is the author of other
books on this subject.

書籍目錄

Preface ixPreliminary Remarks xi1 The Radix-2 Frameworks1.1 Matrix Notation and Algorithms 1.2 The FFT Idea 1.3 The Cooley-Tukey Radix-2 Factorizstion 1.4 Weight and Butterfly Computations1.5 Bit Reversal and Transposition 1.6 The Cooley-Tukey Framework 1.7 The Stockham Autosort Frameworks 1.8 The Pease Framework 1.9 Decimation in Frequency and Inverse FFTs 2 General Radix Frameworks2.1 General Radix Ideas 2.2 Index Reversal and Transposition 2.3 Mixed-Radix Factorizations2.4 Radix-4 and Radix-8 Frameworks2.5 The Spllt-Radix Framework3 High-Performance Frameworks3.1 The Multiple OFT Problem 3.2 Matrix Transposition 3.3 The Large Single-Vector FFT Problem 3.4 The Multidimensional FFT Problem 3.5 Distributed-Memory FFTs 3.6 Shared-Memory FFTs 4 Selected Topics4.1 Prime Factor Frameworks 4.2 Convolution 4.3 FFTs of Real Data 4.4 Fast Trigonometric Transforms 4.5 Fast Poisson SolversBibliographyIndex

媒體關注與評論

"This finely crafted work fills a gap in the library of books on the fast Fourier transform (FFT). It provides a complete and elegant mathematical formulation of the family of algorithms thai compute FFTs. It is written for students and professionals who already have a working knowledge of computational linear algebra... This work is an excellent contribution to the modern FFT literature."　　——J. R. Hubbard, Computing Reviews, September 1993."... An excellent survey on the FFT, which will be valuable to all who wish to use it."　　——S. Hitotumatu, Mathematical Reviews, Issue g3a."...This book contains a very readable and up-to-date　　presentation of FFT techniques, their theory and application. Together with many explicit computational algorithms, the extensive annotated list of references add greatly to the scientific value of this reference text."　　——Short Book Reviews, August 1992, Vol.12, No.2.

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