国际著名数学图书 快速傅里叶变换的计算框架 英文影印版 作者：（美）罗恩 著 出版时间：2011年版 内容简介 the fast fourier transform （fft） family ofalgorithms has revolutionized many areas of scientific computation.the fft is one of the most widely used algorithms in science andengineering， with applications in almost every discipline. thisvolume is the most comprehensive treatment of ffts to date.van loan captures the interplay between mathematics and the designof effective numerical algorithms-a critical connection as moreadvanced machines become available. he uses a stylized matlabnotation， which is familiar to those engaged in high-performancecomputing.this volume is essential for professionals interested in linearalgebra as well as those working with numerical methods. the fft isalso a great vehicle for teaching key aspects of scientificcomputing. 目录 Preface ix Preliminary Remarks xi 1 The Radix-2 Frameworks 1.1 Matrix Notation and Algorithms 2 1.2 The FFT Idea 11 1.3 The Cooley-Tukey Radix-2 Factorizstion 17 1.4 Weight and Butterfly Computations 22 1.5 Bit Reversal and Transposition 36 1.6 The Cooley-Tukey Framework 44 1.7 The Stockham Autosort Frameworks 49 1.8 The Pease Framework 60 1.9 Decimation in Frequency and Inverse FFTs 64 2 General Radix Frameworks 2.1 General Radix Ideas 76 2.2 Index Reversal and Transposition 84 2.3 Mixed-Radix Factorizations 95 2.4 Radix-4 and Radix-8 Frameworks I01 2.5 The Spllt-Radix Framework III 3 High-Performance Frameworks 3.1 The Multiple OFT Problem 122 3.2 Matrix Transposition 125 3.3 The Large Single-Vector FFT Problem 139 3.4 The Multidimensional FFT Problem 148 3.5 Distributed-Memory FFTs 156 3.6 Shared-Memory FFTs 176 4 Selected Topics 4.1 Prime Factor Frameworks 188 4.2 Convolution 205 4.3 FFTs of Real Data 215 4.4 Fast Trigonometric Transforms 229 4.5 Fast Poisson Solvers 247 Bibliography 259 Index 269
