The author captures the interplay between mathematics and the design of effective numerical algorithms.

Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.

This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.

Developing algorithms for multi-dimensional Fourier transforms, this book presents results that yield highly efficient code on a variety of vector and parallel computers. By emphasising the unified basis for the many approaches to both one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimising implementations. It will thus be of great interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing.

Since the publication of the first edition, parallel computing technology has gained considerable momentum. A large proportion of this has come from the improvement in VLSI techniques, offering one to two orders of magnitude more devices than previously possible. A second contributing factor in the fast development of the subject is commercialization. The supercomputer is no longer restricted to a few well-established research institutions and large companies. A new computer breed combining the architectural advantages of the supercomputer with the advance of VLSI technology is now available at very attractive prices. A pioneering device in this development is the transputer, a VLSI processor specifically designed to operate in large concurrent systems. Parallel Computers 2: Architecture, Programming and Algorithms reflects the shift in emphasis of parallel computing and tracks the development of supercomputers in the years since the first edition was published. It looks at large-scale parallelism as found in transputer ensembles. This extensively rewritten second edition includes major new sections on the transputer and the OCCAM language. The book contains specific information on the various types of machines available, details of computer architecture and technologies, and descriptions of programming languages and algorithms. Aimed at an advanced undergraduate and postgraduate level, this handbook is also useful for research workers, machine designers, and programmers concerned with parallel computers. In addition, it will serve as a guide for potential parallel computer users, especially in disciplines where large amounts of computer time are regularly used.

An examination of the use of transputers in numerical computing and neural networks. Topics covered include linear systems of equations and programming, fluid and molecular dynamics simulation, transformations, Kalman filtering and general numerical problems. Neural networks are discussed in ters of algorithms and simulation.

Today all computers, from tablet/desktop computers to super computers, work in parallel. A basic knowledge of the architecture of parallel computers and how to program them, is thus, essential for students of computer science and IT professionals. In its second edition, the book retains the lucidity of the first edition and has added new material to reflect the advances in parallel computers. It is designed as text for the final year undergraduate students of computer science and engineering and information technology. It describes the principles of designing parallel computers and how to program them. This second edition, while retaining the general structure of the earlier book, has added two new chapters, ‘Core Level Parallel Processing’ and ‘Grid and Cloud Computing’ based on the emergence of parallel computers on a single silicon chip popularly known as multicore processors and the rapid developments in Cloud Computing. All chapters have been revised and some chapters are re-written to reflect the emergence of multicore processors and the use of MapReduce in processing vast amounts of data. The new edition begins with an introduction to how to solve problems in parallel and describes how parallelism is used in improving the performance of computers. The topics discussed include instruction level parallel processing, architecture of parallel computers, multicore processors, grid and cloud computing, parallel algorithms, parallel programming, compiler transformations, operating systems for parallel computers, and performance evaluation of parallel computers.