Download or read book A Class of Parallel Methods for Computing a Few Extreme Eigenelements of Large Sparse Matrices Implemented on Parallel Computers written by Sun Kyung Kim and published by . This book was released on 1991 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallelism in Matrix Computations written by Efstratios Gallopoulos and published by Springer. This book was released on 2015-07-25 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book S step Lanczos and Arnoldi Methods on Parallel Computers written by Sun Kyung Kim and published by . This book was released on 1989 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In this paper, we introduce s-step Lanczos and Arnoldi methods for finding a few eigenvalues of a large sparse matrix, and we prove that s-step methods generate reduction matrices which are similar to reduction matrices generated by standard ones. One iteration of s-step Lanczos and Arnoldi algorithms corresponds to s iterations of the standard Lanczos and Arnoldi algorithms, and s-step methods have improved data locality and minimized global communication and superior parallel properties to the standard ones. We implemented s-step Lanczos and Arnoldi methods on CRAY-2 and NCUBE/7 Hypercube and discuss the speedup of s-step methods to the standard ones."
Download or read book Implementation of Some Parallel Algorithms Arising in Sparse Matrix and Other Applications written by David Francis Lass and published by . This book was released on 2017 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally the processing time of a program can be improved by splitting the program into several portions and executing each portion on its own computing core. This process allows us to take advantage of as much of the computer system hardware as we can. However, this also can cause some complexities to arise such as dependency issues. Sparse matrices are, in the most general form, matrices with a large number of zero entries relative to their number of nonzero entries. These matrices are commonly occurring in applications like in a Partial Differential Equation (PDE). Naturally, systems of linear equations involving these sparse matrices are common and there are several methods for solving these systems. As most of these matrices are relatively large, it can be inefficient to solve them directly. Instead many ways to solve these systems involve the use of iterative methods. Combining parallel processing with these iterative methods, we can quickly and efficiently solve large sparse systems. The following thesis contains the use of two types of parallel processing, provides applications of both, shows the value of using iterative methods with sparse matrices, and examines solving partial differential equations using several iterative methods with parallel processing.
Download or read book Parallel Algorithms for Matrix Computations written by K. Gallivan and published by SIAM. This book was released on 1990-01-01 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1991 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1990 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Algorithms for Irregular Problems State of the Art written by Alfonso Ferreira and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Efficient parallel solutions have been found to many problems. Some of them can be obtained automatically from sequential programs, using compilers. However, there is a large class of problems - irregular problems - that lack efficient solutions. IRREGULAR 94 - a workshop and summer school organized in Geneva - addressed the problems associated with the derivation of efficient solutions to irregular problems. This book, which is based on the workshop, draws on the contributions of outstanding scientists to present the state of the art in irregular problems, covering aspects ranging from scientific computing, discrete optimization, and automatic extraction of parallelism. Audience: This first book on parallel algorithms for irregular problems is of interest to advanced graduate students and researchers in parallel computer science.
Download or read book Parallel Processing for Scientific Computing written by G. Rodrigue and published by SIAM. This book was released on 1989-01-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.
Download or read book Advances in Parallel Algorithms written by Ivan Dimov and published by IOS Press. This book was released on 1994 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Basic Sparse Matrix Computations on Massively Parallel Computers written by W. Ferng and published by . This book was released on 1992 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Massively Parallel Sparse matrix Computations written by Institute for Defense Analyses. Supercomputing Research Center and published by . This book was released on 1990 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This paper shows that QR factorization of large, sparse matrices can be performed efficiently on massively-parallel SIMD (Single Instruction stream, Multiple Data stream) computers such as the Connection Machine CM-2. The problem is cast as a dataflow graph, using existing techniques for symbolic manipulation of the structure of the matrix. Then the nodes in the graph, which represent units of computational work, are mapped to a 'virtual dataflow machine' in such a way that only nearest-neighbor communication is required. This virtual machine is implemented by programming the CM-2 processors to support the static dataflow protocol. Execution results for standard test matrices show that good performance is obtained even for 'unstructured' sparsity patterns that are not amenable to nested dissection techniques."
Download or read book Scalable Parallel Algorithms for Sparse Linear Systems written by and published by . This book was released on 1997 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large sparse linear systems occur in many scientific and engineering applications encountered in military and civilian domains. Such systems are typically solved using either iterative or direct methods. We are developing parallel formulations of computationally intensive algorithms that underly these methods. Direct methods for solving sparse linear systems are important because of their generality and robustness. For linear systems arising in certain applications, such as linear programming and some structural engineering applications, they are the only feasible methods. Although highly parallel formulations of dense matrix factorization are well known, it has been a challenge to implement efficient sparse linear system solvers using direct methods, even on moderately parallel computers. We have recently achieved a breakthrough in developing a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems-both in terms of scalability and overall performance. Experiments have shown that this algorithm can easily speedup Cholesky factorization by a factor of at least a few hundred up to 1024 processors, and achieve levels of performance that were unheard of and unimaginable for this problem until very recently.
Download or read book Numerical Analysis and Parallel Processing written by Peter R. Turner and published by Lecture Notes in Mathematics. This book was released on 1989-09-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each week of this three week meeting was a self-contained event, although each had the same underlying theme - the effect of parallel processing on numerical analysis. Each week provided the opportunity for intensive study to broaden participants' research interests or deepen their understanding of topics of which they already had some knowledge. There was also the opportunity for continuing individual research in the stimulating environment created by the presence of several experts of international stature. This volume contains lecture notes for most of the major courses of lectures presented at the meeting; they cover topics in parallel algorithms for large sparse linear systems and optimization, an introductory survey of level-index arithmetic and superconvergence in the finite element method.
Download or read book Introduction to Numerical Methods for Parallel Computers written by Udo Schendel and published by Ellis Horwood. This book was released on 1984 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Sparse Matrix Computations written by Arno C. N. van Duin and published by University of Leiden. This book was released on 1998-01-01 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
