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 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 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 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 Sparse Matrix Computations written by James R. Bunch and published by Academic Press. This book was released on 2014-05-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.

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 Enabling Sparse Matrix Computation in Multi locale Chapel written by Amer Tahir and published by . This book was released on 2016 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving large sparse systems of linear equations is at the core of many problems in scientific computing. Conjugate Gradient (CG), an iterative method, is one of the prominent techniques for solving such systems of the form Ax = b. In addition to many scientific applications, CG is also chosen for high performance benchmarks, i.e. to evaluate the performance of massively parallel computing systems. Traditionally, MPI (Message Passing Interface) based libraries are used to implement CG algorithms, but a new wave of partitioned global address space (PGAS) languages like Chapel are naturally fit for the task. Chapel seeks to provide syntactic and library support for a variety of parallel-programming concepts wherein data-parallel applications are supported via the concepts of domains and distributions. Unlike 'arrays' of traditional languages, Chapel domains are used to represent sets of indices and distributions provide a storage representation for domains, along with their associated arrays of data.

Download or read book Graph Theory and Sparse Matrix Computation written by Alan George and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer, however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. The articles are grouped into three general categories: graph models of symmetric matrices and factorizations, graph models of algorithms on nonsymmetric matrices, and parallel sparse matrix algorithms. This book will be a resource for the researcher or advanced student of either graphs or sparse matrices; it will be useful to mathematicians, numerical analysts and theoretical computer scientists alike.

Download or read book Programming Massively Parallel Processors written by David B. Kirk and published by Newnes. This book was released on 2012-12-31 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Programming Massively Parallel Processors: A Hands-on Approach, Second Edition, teaches students how to program massively parallel processors. It offers a detailed discussion of various techniques for constructing parallel programs. Case studies are used to demonstrate the development process, which begins with computational thinking and ends with effective and efficient parallel programs. This guide shows both student and professional alike the basic concepts of parallel programming and GPU architecture. Topics of performance, floating-point format, parallel patterns, and dynamic parallelism are covered in depth. This revised edition contains more parallel programming examples, commonly-used libraries such as Thrust, and explanations of the latest tools. It also provides new coverage of CUDA 5.0, improved performance, enhanced development tools, increased hardware support, and more; increased coverage of related technology, OpenCL and new material on algorithm patterns, GPU clusters, host programming, and data parallelism; and two new case studies (on MRI reconstruction and molecular visualization) that explore the latest applications of CUDA and GPUs for scientific research and high-performance computing. This book should be a valuable resource for advanced students, software engineers, programmers, and hardware engineers. - New coverage of CUDA 5.0, improved performance, enhanced development tools, increased hardware support, and more - Increased coverage of related technology, OpenCL and new material on algorithm patterns, GPU clusters, host programming, and data parallelism - Two new case studies (on MRI reconstruction and molecular visualization) explore the latest applications of CUDA and GPUs for scientific research and high-performance computing

Download or read book Mapping Unstructured Grid Computations to Massively Parallel Computers written by Steven Warren Hammond and published by . This book was released on 1992 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This thesis investigates the mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time twofold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases."

Download or read book High performance computing for solving large sparse systems Optical diffraction tomography as a case of study written by Gloria Ortega López and published by Universidad Almería. This book was released on 2015-04-14 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis, entitled €High Performance Computing for solving large sparse systems. Optical Diffraction Tomography as a case of study€ investigates the computational issues related to the resolution of linear systems of equations which come from the discretization of physical models described by means of Partial Differential Equations (PDEs). These physical models are conceived for the description of the space-temporary behavior of some physical phenomena f(x, y, z, t) in terms of their variations (partial derivative) with respect to the dependent variables of the phenomena. There is a wide variety of discretization methods for PDEs. Two of the most well-known methods are the Finite Difference Method (FDM) and the Finite Element Method (FEM). Both methods result in an algebraic description of the model that can be translated into the approach of a linear system of equations of type (Ax = b), where A is a sparse matrix (a high percentage of zero elements) whose size depends on the required accuracy of the modeled phenomena. This thesis begins with the algebraic description of the model associated with the physical phenomena, and the work herein has been focused on the design of techniques and computational models that allow the resolution of these linear systems of equations. The main interest of this study is specially focused on models which require a high level of discretization and usually generate sparse matrices, A, which have a highly sparse structure and large size. Literature characterizes these types of problems by their high demanding computational requirements (because of their fine degree of discretization) and the sparsity of the matrices involved, suggesting that these kinds of problems can only be solved using High Performance Computing techniques and architectures. One of the main goals of this thesis is the research of the possible alternatives which allow the implementation of routines to solve large and sparse linear systems of equations using High Performance Computing (HPC). The use of massively parallel platforms (GPUs) allows the acceleration of these routines, because they have several advantages for vectorial computation schemes. On the other hand, the use of distributed memory platforms allows the resolution of problems defined by matrices of enormous size. Finally, the combination of both techniques, distributed computation and multi-GPUs, will allow faster resolution of interesting problems in which large and sparse matrices are involved. In this line, one of the goals of this thesis is to supply the scientific community with implementations based on multi-GPU clusters to solve sparse linear systems of equations, which are the key in many scientific computations. The second part of this thesis is focused on a real physical problem of Optical Diffractional Tomography (ODT) based on holographic information. ODT is a non-damaging technique which allows the extraction of the shapes of objects with high accuracy. Therefore, this technique is very suitable to the in vivo study of real specimens, microorganisms, etc., and it also makes the investigation of their dynamics possible. A preliminary physical model based on a bidimensional reconstruction of the seeding particle distribution in fluids was proposed by J. Lobera and J.M. Coupland. However, its high computational cost (in both memory requirements and runtime) made compulsory the use of HPC techniques to extend the implementation to a three dimensional model. In the second part of this thesis, the implementation and validation of this physical model for the case of three dimensional reconstructions is carried out. In such implementation, the resolution of large and sparse linear systems of equations is required. Thus, some of the algebraic routines developed in the first part of the thesis have been used to implement computational strategies capable of solving the problem of 3D reconstruction based on ODT.

Download or read book Matrix Computations written by Gene H. Golub and published by JHU Press. This book was released on 1996-10-15 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

Download or read book Applied Parallel Computing Computations in Physics Chemistry and Engineering Science written by Jack Dongarra and published by Springer Science & Business Media. This book was released on 1996-02-27 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Second International Workshop on Applied Parallel Computing in Physics, Chemistry and Engineering Science, PARA'95, held in Lyngby, Denmark, in August 1995. The 60 revised full papers included have been contributed by physicists, chemists, and engineers, as well as by computer scientists and mathematicians, and document the successful cooperation of different scientific communities in the booming area of computational science and high performance computing. Many widely-used numerical algorithms and their applications on parallel computers are treated in detail.

Download or read book Direct Methods for Sparse Matrices written by I. S. Duff and published by Oxford University Press. This book was released on 2017-02-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Download or read book Computational Methods for General Sparse Matrices written by Zahari Zlatev and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ... - si j'avait su comment en revenir, One service mathematics has rendered the je n 'y serais point aile.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.

Download or read book Efficient and Parallel Sparse Matrix Computations on the Web written by Prabhjot Sandhu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Large and sparse matrices occur in various scientific and compute-intensive applications, including popular targets such as big-data analytics and machine learning applications. The sparse matrix computations involved in these applications are considered critical for the overall performance due to their recurring nature. At the same time, we are witnessing a surge of such applications on the web due to the ease of accessibility and potential for interactive, collaborative features. In this context, the heavy computation requirements of sparse computations pose a challenge. Recent advancements in JavaScript and WebAssembly engines for web browsers, however, provide opportunities to enable better performance.In this work we present SciWasm.Sparse, a web-based computing framework that offers efficient and scalable sparse matrix CPU kernels to support high-performance computing in web browsers. It provides hand-tuned implementations of Sparse BLAS (Basic Linear Algebra Subroutines) Level 2 operations, element-wise sparse operations, and conversion routines for sparse storage formats. Starting with exploratory research to discover the distinctive nature of the performance of sparse matrix-vector multiplication (SpMV) for WebAssembly compared to native C, we built optimized and parallel SpMV for different sparse storage formats. Our selection of low-level code and data optimization techniques is based on a structure-based performance analysis that identifies several performance bottlenecks via different matrix structure features. We evaluate the performance of our web-based SpMV with its native counterparts from the well-known taco C++ and Intel MKL C libraries on 2000 real-life sparse matrices. We demonstrate that our design can offer performance competitive with even highly tuned and well-established native implementations. Apart from SpMV, we develop a novel and efficient synchronization algorithm for parallel sparse triangular solve (SpTS). It shows impressive performance speedups for a number of matrices over the classic level-set technique. Our framework will facilitate solving large sparse computational problems for performance-critical web applications such as ML frameworks that train and deploy models in the browsers. Our hand-tuned kernels and well-defined parameter space will be valuable for enabling application-specific adaptive capabilities for sparse systems on the web"--

Download or read book Proceedings of the Fourth SIAM Conference on Parallel Processing for Scientific Computing written by J. J. Dongarra and published by SIAM. This book was released on 1990-01-01 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Parallel Computing.