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Author | : Efstratios Gallopoulos |
Publisher | : Springer |
Total Pages | : 489 |
Release | : 2015-07-25 |
Genre | : Technology & Engineering |
ISBN | : 940177188X |
Download Parallelism in Matrix Computations Book in PDF, ePub and Kindle
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.
Author | : K. Gallivan |
Publisher | : SIAM |
Total Pages | : 207 |
Release | : 1990-01-01 |
Genre | : Mathematics |
ISBN | : 9781611971705 |
Download Parallel Algorithms for Matrix Computations Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 197 |
Release | : 1990 |
Genre | : Algorithms |
ISBN | : |
Download Parallel Algorithms for Matrix Computations Book in PDF, ePub and Kindle
Author | : G. W. Stewart |
Publisher | : |
Total Pages | : 8 |
Release | : 1985 |
Genre | : |
ISBN | : |
Download Parallel Matrix Computations Book in PDF, ePub and Kindle
This project concerns the design and analysis of algorithms to be run in a processor-rich environment. It focuses primarily on algorithms that require no global control and that can be run on systems with only local connections among processors. The properties of these algorithms both theoretically and experimentally are investigated. The experimental work is done on the ZMOB, a working parallel computer operated by the Laboratory for Parallel Computation of the Computer Science Department at the University of Maryland. The emphasis is on two areas: 1) Dense problems from numerical linear algebra; and 2) The iterative and direct solution of sparse linear systems. Additional keywords: parallel algorithms; and software development.
Author | : Garry Rodrigue |
Publisher | : Elsevier |
Total Pages | : 416 |
Release | : 2014-05-10 |
Genre | : Reference |
ISBN | : 1483276643 |
Download Parallel Computations Book in PDF, ePub and Kindle
Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed. Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techniques for performing matrix operations on them. The reader is then introduced to FFTs and the tridiagonal linear system as well as the ICCG method. Different versions of the conjugate gradient method for solving the time-dependent diffusion equation are considered. Subsequent chapters deal with two- and three-dimensional fluid flow calculations, paying particular attention to the principal issues in designing efficient numerical methods for hydrodynamic calculations; the decisions that a numerical modeler must make to optimize chemically reactive flow simulations; and how to handle disk-to-core data transfer and storage allocation for the solution of the implicit equations for three-dimensional flows. The book also describes the time-split finite difference scheme for solving the two-dimensional Navier-Stokes equation for flows through slotted nozzles. Finally, the large-scale stimulation of plasmas, as carried out on a small computer with an array processor, is discussed. This monograph should be of interest to specialists in computer science.
Author | : Dimitri Bertsekas |
Publisher | : Athena Scientific |
Total Pages | : 832 |
Release | : 2015-03-01 |
Genre | : Mathematics |
ISBN | : 1886529159 |
Download Parallel and Distributed Computation: Numerical Methods Book in PDF, ePub and Kindle
This highly acclaimed work, first published by Prentice Hall in 1989, is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods. It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms. This is an extensive book, which aside from its focus on parallel and distributed algorithms, contains a wealth of material on a broad variety of computation and optimization topics. It is an excellent supplement to several of our other books, including Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 1999), Dynamic Programming and Optimal Control (Athena Scientific, 2012), Neuro-Dynamic Programming (Athena Scientific, 1996), and Network Optimization (Athena Scientific, 1998). The on-line edition of the book contains a 95-page solutions manual.
Author | : State University of New York at Albany. Dept. of Computer Science |
Publisher | : |
Total Pages | : 29 |
Release | : 1986 |
Genre | : Matrices |
ISBN | : |
Download Complexity of Parallel Matrix Computations Book in PDF, ePub and Kindle
Author | : Seyed H Roosta |
Publisher | : Springer Science & Business Media |
Total Pages | : 579 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461212200 |
Download Parallel Processing and Parallel Algorithms Book in PDF, ePub and Kindle
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.
Author | : George Em Karniadakis |
Publisher | : Cambridge University Press |
Total Pages | : 640 |
Release | : 2003-06-16 |
Genre | : Computers |
ISBN | : 110749477X |
Download Parallel Scientific Computing in C++ and MPI Book in PDF, ePub and Kindle
Numerical algorithms, modern programming techniques, and parallel computing are often taught serially across different courses and different textbooks. The need to integrate concepts and tools usually comes only in employment or in research - after the courses are concluded - forcing the student to synthesise what is perceived to be three independent subfields into one. This book provides a seamless approach to stimulate the student simultaneously through the eyes of multiple disciplines, leading to enhanced understanding of scientific computing as a whole. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems, and parallelization of sparse systems. The material covered is suited to students from engineering, computer science, physics and mathematics.
Author | : Raymond Greenlaw |
Publisher | : Oxford University Press, USA |
Total Pages | : 328 |
Release | : 1995 |
Genre | : Computational complexity |
ISBN | : 0195085914 |
Download Limits to Parallel Computation Book in PDF, ePub and Kindle
This book provides a comprehensive analysis of the most important topics in parallel computation. It is written so that it may be used as a self-study guide to the field, and researchers in parallel computing will find it a useful reference for many years to come. The first half of the book consists of an introduction to many fundamental issues in parallel computing. The second half provides lists of P-complete- and open problems. These lists will have lasting value to researchers in both industry and academia. The lists of problems, with their corresponding remarks, the thorough index, and the hundreds of references add to the exceptional value of this resource. While the exciting field of parallel computation continues to expand rapidly, this book serves as a guide to research done through 1994 and also describes the fundamental concepts that new workers will need to know in coming years. It is intended for anyone interested in parallel computing, including senior level undergraduate students, graduate students, faculty, and people in industry. As an essential reference, the book will be needed in all academic libraries.