Numerical Linear Algebra Digital Signal Processing And Parallel Algorithms

Numerical linear algebra, digital signal processing, and parallel algorithms are three disciplines with a great deal of activity in the last few years. The interaction between them has been growing to a level that merits an Advanced Study Institute dedicated to the three areas together. This volume gives an account of the main results in this interdisciplinary field. The following topics emerged as major themes of the meeting: - Singular value and eigenvalue decompositions, including applications, - Toeplitz matrices, including special algorithms and architectures, - Recursive least squares in linear algebra, digital signal processing and control, - Updating and downdating techniques in linear algebra and signal processing, - Stability and sensitivity analysis of special recursive least squares problems, - Special architectures for linear algebra and signal processing. This book contains tutorials on these topics given by leading scientists in each of the three areas. A consider- able number of new research results are presented in contributed papers. The tutorials and papers will be of value to anyone interested in the three disciplines.

This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers. All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices. Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for parallel shared-memory systems, and the design of fast algorithms and implementations for vector supercomputers.

Aims to bridge the gap between parallel computer architectures and the creation of parallel digital signal processing (DSP) algorithms. This work offers an approach to digital signal processing utilizing the unified signal algebra environment to develop naturally occurring parallel DSP algorithms.;College or university book shops may order five or more copies at a special student price. Price is available on request.

Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.

Over the past few years, the demand for high speed Digital Signal Proces sing (DSP) has increased dramatically. New applications in real-time image processing, satellite communications, radar signal processing, pattern recogni tion, and real-time signal detection and estimation require major improvements at several levels; algorithmic, architectural, and implementation. These perfor mance requirements can be achieved by employing parallel processing at all levels. Very Large Scale Integration (VLSI) technology supports and provides a good avenue for parallelism. Parallelism offers efficient sohitions to several problems which can arise in VLSI DSP architectures such as: 1. Intermediate data communication and routing: several DSP algorithms, such as FFT, involve excessive data routing and reordering. Parallelism is an efficient mechanism to minimize the silicon cost and speed up the pro cessing time of the intermediate middle stages. 2. Complex DSP applications: the required computation is almost doubled. Parallelism will allow two similar channels processing at the same time. The communication between the two channels has to be minimized. 3. Applicatilm specific systems: this emerging approach should achieve real-time performance in a cost-effective way. 4. Testability and fault tolerance: reliability has become a required feature in most of DSP systems. To achieve such property, the involved time overhead is significant. Parallelism may be the solution to maintain ac ceptable speed performance.

An undergraduate textbook that highlights motivating applications and contains summary sections, examples, exercises, online MATLAB codes and a MATLAB toolkit. All the major topics of computational linear algebra are covered, from basic concepts to advanced topics such as the quadratic eigenvalue problem in later chapters.

This text presents an overview of research in the subjects of computational linear algebra, Monte Carlo algorithms and parallel algorithms in discrete mathematics. Topics covered include theoretical investigations of numerical analysis and parallel algorithms, and practical large-scale problem solving such as modelling of semiconductor devices, ballistic trajectory estimations and the simulation of distributed memory parallel computers.