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Loan C. — Computational Frameworks for the Fast Fourier Transform (Frontiers in Applied Mathematics)
Loan C. — Computational Frameworks for the Fast Fourier Transform (Frontiers in Applied Mathematics)



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Название: Computational Frameworks for the Fast Fourier Transform (Frontiers in Applied Mathematics)

Автор: Loan C.

Аннотация:

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. A stylized Matlab notation, which is familiar to those engaged in high-performance computing, is used. 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 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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 287

Добавлена в каталог: 21.02.2015

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Software      xii—xiii
Sparse factorization idea      17—18
Speed of fast Fourier transforms      15
Speedup      168
Split-radix, butterfly      113
Split-radix, computation tree      114
Split-radix, derivation      115—118
Split-radix, flop analysis      119
Split-radix, framework      118
Split-radix, recursive specification      115
Split-radix, splitting      111—113
Splitting factors      95
Splitting, radix-2      12—14
Splitting, radix-p      78—80
Splitting, split-radix      111—113
Stockham framework, mixed-radix      95—96 100—101
Stockham framework, multiple DFTs and      122—123
Stockham framework, radix-2      49ff
Stockham framework, radix-4      105—106
Stride      31—32 45 125
Structured splitting framework      243—245
SubMatrix      4
Three-dimensional FFT      150—152
Toeplitz matrix, definition      208
Toeplitz matrix, times vector      209
Trace      213
Transposed Stockham framework, mixed-radix      95—96 98
Transposed Stockham framework, radix-2      50ff
Transposed Stockham framework, shared-memory      179—181
Transposition and memory bank conflict      126
Transposition by diagonal      126
Transposition by permutation cycles      127
Transposition in hierarchical memory      127ff
Transposition, distributed-memory      169
Transposition, Fraser      133—138
Transposition, scalar      126
Transposition, shared-memory      182—183
Truncated Stockham framework      125
Twiddle-factor methods      see "Four-step or six-step frameworks"
Twiddle-factor scaling, blocking      142
Twiddle-factor scaling, definition of      139
Two-dimensional convolution      212—214
Two-dimensional DFT and bit-reversal      150
Two-dimensional FFT      148ff
Unit roundoff      23
Unit stride      57—58 125
Vector computer      9
Vector length      57—58 122
Vector operations      9
Vector performance      33—34
Vector symmetries      234
Vector-radix framework      148—150
Vectorization      34
Weight precomputation in radix-4 setting      106—107
Weight precomputation, direct call      23
Weight precomputation, forward recursion      25
Weight precomputation, Givens rotations and      24—25
Weight precomputation, logarithmic recursion      26
Weight precomputation, long weight vector      34—35
Weight precomputation, off-line      30—31
Weight precomputation, on-line      30—31
Weight precomputation, recursive bisection      27
Weight precomputation, repeated multiplication      24
Weight precomputation, roundoff error and      22ff 28
Weight precomputation, stability and      28
Weight precomputation, subvector scaling      24
Weight vector symmetries      28
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