Graph Theory And Sparse Matrix Computation

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Graph Theory and Sparse Matrix Computation

Author : Alan George
Publisher : Springer Science & Business Media
ISBN 13 : 1461383692
Total Pages : 254 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Graph Theory and Sparse Matrix Computation by : Alan George

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.

Graph Theory and Sparse Matrix Computation

Author : Alan George
Publisher : Springer
ISBN 13 : 9780387941318
Total Pages : 245 pages
Book Rating : 4.9/5 (413 download)

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Book Synopsis Graph Theory and Sparse Matrix Computation by : Alan George

Download or read book Graph Theory and Sparse Matrix Computation written by Alan George and published by Springer. This book was released on 1993-10-22 with total page 245 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.

Graph Algorithms in the Language of Linear Algebra

Author : Jeremy Kepner
Publisher : SIAM
ISBN 13 : 9780898719918
Total Pages : 388 pages
Book Rating : 4.7/5 (199 download)

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Book Synopsis Graph Algorithms in the Language of Linear Algebra by : Jeremy Kepner

Download or read book Graph Algorithms in the Language of Linear Algebra written by Jeremy Kepner and published by SIAM. This book was released on 2011-01-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Direct Methods for Sparse Linear Systems

Author : Timothy A. Davis
Publisher : SIAM
ISBN 13 : 0898716136
Total Pages : 228 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Direct Methods for Sparse Linear Systems by : Timothy A. Davis

Download or read book Direct Methods for Sparse Linear Systems written by Timothy A. Davis and published by SIAM. This book was released on 2006-09-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computer Solution of Large Sparse Positive Definite Systems

Author : Alan George
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Computer Solution of Large Sparse Positive Definite Systems by : Alan George

Download or read book Computer Solution of Large Sparse Positive Definite Systems written by Alan George and published by Prentice Hall. This book was released on 1981 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Iterative Methods for Sparse Linear Systems

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Sparse Matrix Technology - electronic edition

Author : Sergio Pissanetzky
Publisher :
ISBN 13 : 0976277530
Total Pages : 324 pages
Book Rating : 4.9/5 (762 download)

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Book Synopsis Sparse Matrix Technology - electronic edition by : Sergio Pissanetzky

Download or read book Sparse Matrix Technology - electronic edition written by Sergio Pissanetzky and published by . This book was released on 1984 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algorithms for Sparse Linear Systems

Author : Jennifer Scott
Publisher : Springer Nature
ISBN 13 : 3031258207
Total Pages : 254 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Algorithms for Sparse Linear Systems by : Jennifer Scott

Download or read book Algorithms for Sparse Linear Systems written by Jennifer Scott and published by Springer Nature. This book was released on 2023-04-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sparse Matrices and their Applications

Author : D. Rose
Publisher : Springer Science & Business Media
ISBN 13 : 1461586755
Total Pages : 215 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Sparse Matrices and their Applications by : D. Rose

Download or read book Sparse Matrices and their Applications written by D. Rose and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Iain S. Duff
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Direct Methods for Sparse Matrices by : Iain S. Duff

Download or read book Direct Methods for Sparse Matrices written by Iain S. Duff and published by Oxford University Press, USA. This book was released on 1986 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Direct Methods for Sparse Matrices

Author : Iain S. Duff
Publisher : Oxford University Press
ISBN 13 : 0198508387
Total Pages : 451 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Direct Methods for Sparse Matrices by : Iain S. Duff

Download or read book Direct Methods for Sparse Matrices written by Iain S. Duff and published by Oxford University Press. This book was released on 2017 with total page 451 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 millionin 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 inthe 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 ofthe authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Combinatorial Scientific Computing

Author : Uwe Naumann
Publisher : CRC Press
ISBN 13 : 1439827362
Total Pages : 584 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Combinatorial Scientific Computing by : Uwe Naumann

Download or read book Combinatorial Scientific Computing written by Uwe Naumann and published by CRC Press. This book was released on 2012-01-25 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Chordal Graphs and Semidefinite Optimization

Author : Lieven Vandenberghe
Publisher : Foundations and Trends (R) in Optimization
ISBN 13 : 9781680830385
Total Pages : 216 pages
Book Rating : 4.8/5 (33 download)

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Book Synopsis Chordal Graphs and Semidefinite Optimization by : Lieven Vandenberghe

Download or read book Chordal Graphs and Semidefinite Optimization written by Lieven Vandenberghe and published by Foundations and Trends (R) in Optimization. This book was released on 2015-04-30 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the theory and applications of chordal graphs, with an emphasis on algorithms developed in the literature on sparse Cholesky factorization. It shows how these techniques can be applied in algorithms for sparse semidefinite optimization, and points out the connections with related topics outside semidefinite optimization.

Computational Methods for Large Sparse Power Systems Analysis

Author : S.A. Soman
Publisher : Springer Science & Business Media
ISBN 13 : 1461508231
Total Pages : 349 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Computational Methods for Large Sparse Power Systems Analysis by : S.A. Soman

Download or read book Computational Methods for Large Sparse Power Systems Analysis written by S.A. Soman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational methods in Power Systems require significant inputs from diverse disciplines, such as data base structures, numerical analysis etc. Strategic decisions in sparsity exploitation and algorithm design influence large-scale simulation and high-speed computations. Selection of programming paradigm shapes the design, its modularity and reusability. This has a far reaching effect on software maintenance. Computational Methods for Large Sparse Power Systems Analysis: An Object Oriented Approach provides a unified object oriented (OO) treatment for power system analysis. Sparsity exploitation techniques in OO paradigm are emphasized to facilitate large scale and fast computing. Specific applications like large-scale load flow, short circuit analysis, state estimation and optimal power flow are discussed within this framework. A chapter on modeling and computational issues in power system dynamics is also included. Motivational examples and illustrations are included throughout the book. A library of C++ classes provided along with this book has classes for transmission lines, transformers, substation etc. A CD-ROM with C++ programs is also included. It contains load flow, short circuit analysis and network topology processor applications. Power system data is provided and systems up to 150 buses can be studied. Other Special Features: This book is the first of its kind, covering power system applications designed with an OO perspective. Chapters on object orientation for modeling of power system computations, data structure, large sparse linear system solver, sparse QR decomposition in an OO framework are special features of this book.

Handbook of Data Structures and Applications

Author : Dinesh P. Mehta
Publisher : Taylor & Francis
ISBN 13 : 1498701884
Total Pages : 1120 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Data Structures and Applications by : Dinesh P. Mehta

Download or read book Handbook of Data Structures and Applications written by Dinesh P. Mehta and published by Taylor & Francis. This book was released on 2018-02-21 with total page 1120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Data Structures and Applications was first published over a decade ago. This second edition aims to update the first by focusing on areas of research in data structures that have seen significant progress. While the discipline of data structures has not matured as rapidly as other areas of computer science, the book aims to update those areas that have seen advances. Retaining the seven-part structure of the first edition, the handbook begins with a review of introductory material, followed by a discussion of well-known classes of data structures, Priority Queues, Dictionary Structures, and Multidimensional structures. The editors next analyze miscellaneous data structures, which are well-known structures that elude easy classification. The book then addresses mechanisms and tools that were developed to facilitate the use of data structures in real programs. It concludes with an examination of the applications of data structures. Four new chapters have been added on Bloom Filters, Binary Decision Diagrams, Data Structures for Cheminformatics, and Data Structures for Big Data Stores, and updates have been made to other chapters that appeared in the first edition. The Handbook is invaluable for suggesting new ideas for research in data structures, and for revealing application contexts in which they can be deployed. Practitioners devising algorithms will gain insight into organizing data, allowing them to solve algorithmic problems more efficiently.

High Performance Computing for Computational Science - VECPAR 2006

Author : Michel Daydé
Publisher : Springer
ISBN 13 : 3540713514
Total Pages : 728 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis High Performance Computing for Computational Science - VECPAR 2006 by : Michel Daydé

Download or read book High Performance Computing for Computational Science - VECPAR 2006 written by Michel Daydé and published by Springer. This book was released on 2007-05-30 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on High Performance Computing for Computational Science, VECPAR 2006, held in Rio de Janeiro, Brazil, in June 2006. The 44 revised full papers presented together with one invited paper and 12 revised workshop papers cover Grid computing, cluster computing, numerical methods, large-scale simulations in Physics, and computing in Biosciences.

Algorithms - ESA 2009

Author : Amos Fiat
Publisher : Springer Science & Business Media
ISBN 13 : 3642041272
Total Pages : 807 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Algorithms - ESA 2009 by : Amos Fiat

Download or read book Algorithms - ESA 2009 written by Amos Fiat and published by Springer Science & Business Media. This book was released on 2009-09-03 with total page 807 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th Annual European Symposium on Algorithms, ESA 2009, held in Copenhagen, Denmark, in September 2009 in the context of the combined conference ALGO 2009. The 67 revised full papers presented together with 3 invited lectures were carefully reviewed and selected: 56 papers out of 222 submissions for the design and analysis track and 10 out of 36 submissions in the engineering and applications track. The papers are organized in topical sections on trees, geometry, mathematical programming, algorithmic game theory, navigation and routing, graphs and point sets, bioinformatics, wireless communiations, flows, matrices, compression, scheduling, streaming, online algorithms, bluetooth and dial a ride, decomposition and covering, algorithm engineering, parameterized algorithms, data structures, and hashing and lowest common ancestor.