Sparse Matrix Computations
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| Author | : James R. Bunch |
| Publisher | : Academic Press |
| Total Pages | : 468 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483263401 |
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.
| Author | : Alan George |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 254 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461383692 |
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.
| Author | : Timothy A. Davis |
| Publisher | : SIAM |
| Total Pages | : 228 |
| Release | : 2006-09-01 |
| Genre | : Computers |
| ISBN | : 0898716136 |
The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.
| Author | : Gene Howard Golub |
| Publisher | : |
| Total Pages | : 476 |
| Release | : 1983 |
| Genre | : Matrices |
| ISBN | : 9780946536054 |
| Author | : K. Gallivan |
| Publisher | : SIAM |
| Total Pages | : 207 |
| Release | : 1990-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971705 |
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 | : Yousef Saad |
| Publisher | : SIAM |
| Total Pages | : 537 |
| Release | : 2003-04-01 |
| Genre | : Mathematics |
| ISBN | : 0898715342 |
Mathematics of Computing -- General.
| Author | : Hamid Sarbazi-Azad |
| Publisher | : Morgan Kaufmann |
| Total Pages | : 776 |
| Release | : 2016-09-15 |
| Genre | : Computers |
| ISBN | : 0128037881 |
Advances in GPU Research and Practice focuses on research and practices in GPU based systems. The topics treated cover a range of issues, ranging from hardware and architectural issues, to high level issues, such as application systems, parallel programming, middleware, and power and energy issues. Divided into six parts, this edited volume provides the latest research on GPU computing. Part I: Architectural Solutions focuses on the architectural topics that improve on performance of GPUs, Part II: System Software discusses OS, compilers, libraries, programming environment, languages, and paradigms that are proposed and analyzed to help and support GPU programmers. Part III: Power and Reliability Issues covers different aspects of energy, power, and reliability concerns in GPUs. Part IV: Performance Analysis illustrates mathematical and analytical techniques to predict different performance metrics in GPUs. Part V: Algorithms presents how to design efficient algorithms and analyze their complexity for GPUs. Part VI: Applications and Related Topics provides use cases and examples of how GPUs are used across many sectors. - Discusses how to maximize power and obtain peak reliability when designing, building, and using GPUs - Covers system software (OS, compilers), programming environments, languages, and paradigms proposed to help and support GPU programmers - Explains how to use mathematical and analytical techniques to predict different performance metrics in GPUs - Illustrates the design of efficient GPU algorithms in areas such as bioinformatics, complex systems, social networks, and cryptography - Provides applications and use case scenarios in several different verticals, including medicine, social sciences, image processing, and telecommunications
| Author | : David B. Kirk |
| Publisher | : Newnes |
| Total Pages | : 519 |
| Release | : 2012-12-31 |
| Genre | : Computers |
| ISBN | : 0123914183 |
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
| Author | : Zhong-Zhi Bai |
| Publisher | : SIAM |
| Total Pages | : 496 |
| Release | : 2021-09-09 |
| Genre | : Mathematics |
| ISBN | : 1611976634 |
This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics
| Author | : Åke Björck |
| Publisher | : Springer |
| Total Pages | : 812 |
| Release | : 2014-10-07 |
| Genre | : Mathematics |
| ISBN | : 3319050893 |
Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.
