Graph Theory And Sparse Matrix Computation
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Graph Theory And Sparse Matrix Computation
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Author : Alan George
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Graph Theory And Sparse Matrix Computation written by Alan George and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Graph Theory And Sparse Matrix Computation
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Author : Alan George
language : en
Publisher: Springer
Release Date : 1993-10-22
Graph Theory And Sparse Matrix Computation written by Alan George and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-22 with Mathematics categories.
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.
Direct Methods For Sparse Linear Systems
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Author : Timothy A. Davis
language : en
Publisher: SIAM
Release Date : 2006-09-01
Direct Methods For Sparse Linear Systems written by Timothy A. Davis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-01 with Computers categories.
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.
Direct Methods For Sparse Matrices
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Author : I. S. Duff
language : en
Publisher: Oxford University Press
Release Date : 2017-03-09
Direct Methods For Sparse Matrices written by I. S. Duff and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-09 with Mathematics categories.
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.
Graph Algorithms In The Language Of Linear Algebra
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Author : Jeremy Kepner
language : en
Publisher: SIAM
Release Date : 2011-01-01
Graph Algorithms In The Language Of Linear Algebra written by Jeremy Kepner and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.
Algorithms And Computation
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Author : Takao Asano
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-21
Algorithms And Computation written by Takao Asano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-21 with Computers categories.
This book constitutes the refereed proceedings of the 22nd International Symposium on Algorithms and Computation, ISAAC 2011, held in Yokohama, Japan in December 2011. The 76 revised full papers presented together with two invited talks were carefully reviewed and selected from 187 submissions for inclusion in the book. This volume contains topics such as approximation algorithms; computational geometry; computational biology; computational complexity; data structures; distributed systems; graph algorithms; graph drawing and information visualization; optimization; online and streaming algorithms; parallel and external memory algorithms; parameterized algorithms; game theory and internet algorithms; randomized algorithms; and string algorithms.
Combinatorial Scientific Computing
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Author : Uwe Naumann
language : en
Publisher: CRC Press
Release Date : 2012-01-25
Combinatorial Scientific Computing written by Uwe Naumann and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-25 with Computers categories.
Combinatorial Scientific Computing explores the latest research on creating algorithms and software tools to solve key combinatorial problems on large-scale high-performance computing architectures. It includes contributions from international researchers who are pioneers in designing software and applications for high-performance computing systems. The book offers a state-of-the-art overview of the latest research, tool development, and applications. It focuses on load balancing and parallelization on high-performance computers, large-scale optimization, algorithmic differentiation of numerical simulation code, sparse matrix software tools, and combinatorial challenges and applications in large-scale social networks. The authors unify these seemingly disparate areas through a common set of abstractions and algorithms based on combinatorics, graphs, and hypergraphs. Combinatorial algorithms have long played a crucial enabling role in scientific and engineering computations and their importance continues to grow with the demands of new applications and advanced architectures. By addressing current challenges in the field, this volume sets the stage for the accelerated development and deployment of fundamental enabling technologies in high-performance scientific computing.
Algorithms And Computation
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Author : Toshihide Ibaraki
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-03
Algorithms And Computation written by Toshihide Ibaraki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-03 with Computers categories.
This book constitutes the refereed proceedings of the 14th International Symposium on Algorithms and Computation, ISAAC 2003, held in Kyoto, Japan, in December 2003. The 73 revised full papers presented were carefully reviewed and selected from 207 submissions. The papers are organized in topical sections on computational geometry, graph and combinatorial algorithms, computational complexity, quantum computing, combinatorial optimization, scheduling, computational biology, distributed and parallel algorithms, data structures, combinatorial and network optimization, computational complexity and cryptography, game theory and randomized algorithms, and algebraic and arithmetic computation.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Algorithms And Computation
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Author : Takeshi Tokuyama
language : en
Publisher: Springer
Release Date : 2007-12-06
Algorithms And Computation written by Takeshi Tokuyama and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-06 with Computers categories.
This book constitutes the refereed proceedings of the 18th International Symposium on Algorithms and Computation, ISAAC 2007, held in Sendai, Japan, in December 2007. The 77 revised full papers presented together with two invited talks were carefully reviewed and selected from 220 submissions. The papers included topical sections on graph algorithms, computational geometry, complexity, graph drawing, distributed algorithms, optimization, data structure, and game theory.