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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.
Matrix Singular Value Decomposition (SVD) and its application to problems in signal processing is explored in this book. The papers discuss algorithms and implementation architectures for computing the SVD, as well as a variety of applications such as systems and signal modeling and detection.The publication presents a number of keynote papers, highlighting recent developments in the field, namely large scale SVD applications, isospectral matrix flows, Riemannian SVD and consistent signal reconstruction. It also features a translation of a historical paper by Eugenio Beltrami, containing one of the earliest published discussions of the SVD.With contributions sourced from internationally recognised scientists, the book will be of specific interest to all researchers and students involved in the SVD and signal processing field.
This volume is an outgrowth of the 2nd International Workshop on SVD and Signal Processing which was held in Kingston, Rhode Island, 25-27 June, 1990. The singular value decomposition (SVD) has been applied to signal processing problems since the late 1970's, although it has been known in various forms for over 100 years. SVD filtering has been shown to give better results at lower signal-to-noise ratios than classical techniques based on linear filtering. This explains in part the recent interest in SVD techniques for signal processing. This book is a compilation of papers that examine in detail the singular decomposition of a matrix and its application to problems in signal processing. Algorithms and implementation architectures for computing the SVD are discussed, and analysis techniques for predicting and understanding the performance of SVD-based algorithms are given. The volume will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
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.
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.