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.

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.

Sparse Matrices And Their Applications

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Author : D. Rose
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Sparse Matrices And Their Applications written by D. Rose 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 Science categories.

This book contains papers on sparse matrices and their appli cations which were presented at a Symposium held at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York on September 9-10, 1971. This is a very active field of research since efficient techniques for handling sparse matrix calculations are an important aspect of problem solving. In large scale problems, the feasibility of the calculation depends critically on the efficiency of the underlying sparse matrix algorithms. An important feature of the conference and its proceedings is the cross-fertilization achieved among a broad spectrum of application areas, and among combinatorialists, numerical analysts, and computer scientists. The mathematical, programming, and data management features of these techniques provide a unifying theme which can benefit readers in many fields. The introduction summarizes the major ideas in each paper. These ideas are interspersed with a brief survey of sparse matrix technology. An extensive unified bibliography is provided for the reader interested in more systematic information. The editors wish to thank Robert K. Brayton for his many helpful suggestions as chairman of the organizing committee and Redmond O'Brien for his editorial and audio-visual assistance. We would also like to thank Mrs. Tiyo Asai and Mrs. Joyce Otis for their help during the conference and on the numerous typing jobs for the manuscript. A special thanks goes to William J. Turner for establishing the IBM Research Symposia Series with Plenum Press.

Direct Methods For Sparse Matrices

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Author : Iain S. Duff
language : en
Publisher: Oxford University Press, USA
Release Date : 1986

Direct Methods For Sparse Matrices written by Iain S. Duff and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Language Arts & Disciplines categories.

This subject has its roots 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.

Algorithms For Sparse Linear Systems

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Author : Jennifer Scott
language : en
Publisher: Springer Nature
Release Date : 2023-04-29

Algorithms For Sparse Linear Systems written by Jennifer Scott and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Mathematics categories.

Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

Computer Solution Of Large Sparse Positive Definite Systems

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Author : Alan George
language : en
Publisher: Prentice Hall
Release Date : 1981

Computer Solution Of Large Sparse Positive Definite Systems written by Alan George and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

Sparse Matrices And Graph Theory

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Author : Kuo-Young Cheng
language : en
Publisher:
Release Date : 1972

Sparse Matrices And Graph Theory written by Kuo-Young Cheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Graph theory categories.

The Efficient Computation Of Sparse Jacobian Matrices Using Automatic Differentiation

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Author : Thomas Frederick Coleman
language : en
Publisher:
Release Date : 1995

The Efficient Computation Of Sparse Jacobian Matrices Using Automatic Differentiation written by Thomas Frederick Coleman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Differential calculus categories.

Algebraic Graph Algorithms

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Author : K. Erciyes
language : en
Publisher: Springer Nature
Release Date : 2021-11-17

Algebraic Graph Algorithms written by K. Erciyes and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-17 with Computers categories.

This textbook discusses the design and implementation of basic algebraic graph algorithms, and algebraic graph algorithms for complex networks, employing matroids whenever possible. The text describes the design of a simple parallel matrix algorithm kernel that can be used for parallel processing of algebraic graph algorithms. Example code is presented in pseudocode, together with case studies in Python and MPI. The text assumes readers have a background in graph theory and/or graph algorithms.