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Author: Publisher: ISBN: Category : Languages : en Pages : 11
Book Description
The efficiency of a parallel implementation of the conjugate gradient method preconditioned by an incomplete Cholesky factorization can vary dramatically depending on the column ordering chosen. One method to minimize the number of major parallel steps is to choose an ordering based on a coloring of the symmetric graph representing the nonzero adjacency structure of the matrix. In this paper, we compare the performance of the preconditioned conjugate gradient method using these coloring orderings with a number of standard orderings on matrices arising from applications in structural engineering. Because optimal colorings for these systems may not be a priori known: we employ several graph coloring heuristics to obtain consistent colorings. Based on lower bounds obtained from the local structure of these systems, we find that the colorings determined by these heuristics are nearly optimal. For these problems, we find that the increase in parallelism afforded by the coloring-based orderings more than offsets any increase in the number of iterations required for the convergence of the conjugate gradient algorithm.
Author: Publisher: ISBN: Category : Languages : en Pages : 11
Book Description
The efficiency of a parallel implementation of the conjugate gradient method preconditioned by an incomplete Cholesky factorization can vary dramatically depending on the column ordering chosen. One method to minimize the number of major parallel steps is to choose an ordering based on a coloring of the symmetric graph representing the nonzero adjacency structure of the matrix. In this paper, we compare the performance of the preconditioned conjugate gradient method using these coloring orderings with a number of standard orderings on matrices arising from applications in structural engineering. Because optimal colorings for these systems may not be a priori known: we employ several graph coloring heuristics to obtain consistent colorings. Based on lower bounds obtained from the local structure of these systems, we find that the colorings determined by these heuristics are nearly optimal. For these problems, we find that the increase in parallelism afforded by the coloring-based orderings more than offsets any increase in the number of iterations required for the convergence of the conjugate gradient algorithm.
Author: David A. Bader Publisher: CRC Press ISBN: 1000538613 Category : Business & Economics Languages : en Pages : 632
Book Description
"Graphs. Such a simple idea. Map a problem onto a graph then solve it by searching over the graph or by exploring the structure of the graph. What could be easier? Turns out, however, that working with graphs is a vast and complex field. Keeping up is challenging. To help keep up, you just need an editor who knows most people working with graphs, and have that editor gather nearly 70 researchers to summarize their work with graphs. The result is the book Massive Graph Analytics." — Timothy G. Mattson, Senior Principal Engineer, Intel Corp Expertise in massive-scale graph analytics is key for solving real-world grand challenges from healthcare to sustainability to detecting insider threats, cyber defense, and more. This book provides a comprehensive introduction to massive graph analytics, featuring contributions from thought leaders across academia, industry, and government. Massive Graph Analytics will be beneficial to students, researchers, and practitioners in academia, national laboratories, and industry who wish to learn about the state-of-the-art algorithms, models, frameworks, and software in massive-scale graph analytics.
Author: Alan George Publisher: Springer Science & Business Media ISBN: 1461383692 Category : Mathematics Languages : en Pages : 254
Book Description
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 ISBN: 0898716136 Category : Computers Languages : en Pages : 228
Book Description
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: W.H.A. SCHILDERS Publisher: Elsevier ISBN: 0080459153 Category : Mathematics Languages : en Pages : 930
Book Description
This special volume provides a broad overview and insight in the way numerical methods are being used to solve the wide variety of problems in the electronics industry. Furthermore its aim is to give researchers from other fields of application the opportunity to benefit from the results wich have been obtained in the electronics industry. * Complete survey of numerical methods used in the electronic industry* Each chapter is selfcontained* Presents state-of-the-art applications and methods* Internationally recognised authors
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Author: David A. Bader
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Author: Timothy A. Davis
Author: W.H.A. SCHILDERS
Author: Assefaw Hadish Gebremedhin