Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details
on FFT for parallel computers. FFT is an efficient implementation of the discrete Fourier transform (DFT), and is widely used
for many applications in engineering, science, and mathematics. Presenting many algorithms in pseudo-code and a complexity
analysis, this book offers a valuable reference guide for graduate students, engineers, and scientists in the field who wish
to apply FFT to large-scale problems.Parallel computation is becoming indispensable in solving the large-scale problems increasingly
arising in a wide range of applications. The performance of parallel supercomputers is steadily improving, and it is expected
that a massively parallel system with hundreds of thousands of compute nodes equipped with multi-core processors and accelerators
will be available in the near future. Accordingly, the book also provides up-to-date computational techniques relevant to
the FFT in state-of-the-art parallel computers.
Following the introductory chapter, Chapter 2 introduces
readers to the DFT and the basic idea of the FFT. Chapter 3 explains mixed-radix FFT algorithms, while Chapter 4 describes
split-radix FFT algorithms. Chapter 5 explains multi-dimensional FFT algorithms, Chapter 6 presents high-performance FFT algorithms,
and Chapter 7 addresses parallel FFT algorithms for shared-memory parallel computers. In closing, Chapter 8 describes parallel
FFT algorithms for distributed-memory parallel computers.