Parallel Algorithms And Matrix Computation

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.

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.

One of the first textbooks on the topic, this book brings together and further articulates the fundamental concepts in parallel computing. It covers the application of parallel algorithms to numerical linear algebra, with an emphasis on the design and analysis of algorithms that are of particular importance in both industrial and academic research. The first part is devoted to a discussion of the general principles and techniques involved, and is illustrated by numerous examples. Dr. Modi goes on to describe some key areas of application, such as sorting, linear systems, partial differential equations, singular-value decomposition, and eigenvalue analysis. Based on a lecture course at the University of Cambridge, the text will appeal to those with an interest in the design and implementations of algorithms in parallel computing.

Motivation It is now possible to build powerful single-processor and multiprocessor systems and use them efficiently for data processing, which has seen an explosive ex pansion in many areas of computer science and engineering. One approach to meeting the performance requirements of the applications has been to utilize the most powerful single-processor system that is available. When such a system does not provide the performance requirements, pipelined and parallel process ing structures can be employed. The concept of parallel processing is a depar ture from sequential processing. In sequential computation one processor is in volved and performs one operation at a time. On the other hand, in parallel computation several processors cooperate to solve a problem, which reduces computing time because several operations can be carried out simultaneously. Using several processors that work together on a given computation illustrates a new paradigm in computer problem solving which is completely different from sequential processing. From the practical point of view, this provides sufficient justification to investigate the concept of parallel processing and related issues, such as parallel algorithms. Parallel processing involves utilizing several factors, such as parallel architectures, parallel algorithms, parallel programming lan guages and performance analysis, which are strongly interrelated. In general, four steps are involved in performing a computational problem in parallel. The first step is to understand the nature of computations in the specific application domain.

Parallel Scientific Computing and Optimization introduces new developments in the construction, analysis, and implementation of parallel computing algorithms. This book presents 23 self-contained chapters, including survey chapters and surveys, written by distinguished researchers in the field of parallel computing. Each chapter is devoted to some aspects of the subject: parallel algorithms for matrix computations, parallel optimization, management of parallel programming models and data, with the largest focus on parallel scientific computing in industrial applications. This volume is intended for scientists and graduate students specializing in computer science and applied mathematics who are engaged in parallel scientific computing.

Mathematics of Computing -- Parallelism.

An introduction to parallel computation and the application of parallel algorithms to numerical linear algebra, based on a lecture course at the University of Cambridge. The emphasis is on the design and analysis of algorithms which are of importance to industrial and academic research.