Graph Theory And Sparse Matrix Computation

Author : Alan George,John R. Gilbert,Joseph W.H. Liu
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461383697

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Graph Theory and Sparse Matrix Computation by Alan George,John R. Gilbert,Joseph W.H. Liu Pdf

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 : Alan George,John R. Gilbert,Joseph W.H. Liu
Publisher : Springer
Page : 245 pages
File Size : 47,6 Mb
Release : 1993-10-22
Category : Mathematics
ISBN : 0387941312

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Graph Theory and Sparse Matrix Computation by Alan George,John R. Gilbert,Joseph W.H. Liu Pdf

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 : Jeremy Kepner,John Gilbert
Publisher : SIAM
Page : 388 pages
File Size : 48,7 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 0898719917

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Graph Algorithms in the Language of Linear Algebra by Jeremy Kepner,John Gilbert Pdf

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.

Author : Sergio Pissanetzky
Publisher : Unknown
Page : 324 pages
File Size : 48,6 Mb
Release : 1984
Category : Electronic
ISBN : 9780976277538

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Sparse Matrix Technology - electronic edition by Sergio Pissanetzky Pdf

Author : Iain S. Duff,A. M. Erisman,John Ker Reid
Publisher : Oxford University Press
Page : 451 pages
File Size : 55,9 Mb
Release : 2017
Category : Electronic book
ISBN : 9780198508380

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Direct Methods for Sparse Matrices by Iain S. Duff,A. M. Erisman,John Ker Reid Pdf

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.

Author : Jennifer Scott,Miroslav Tůma
Publisher : Springer Nature
Page : 254 pages
File Size : 49,6 Mb
Release : 2023-04-29
Category : Mathematics
ISBN : 9783031258206

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Algorithms for Sparse Linear Systems by Jennifer Scott,Miroslav Tůma Pdf

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.

Author : Uwe Naumann,Olaf Schenk
Publisher : CRC Press
Page : 584 pages
File Size : 54,5 Mb
Release : 2012-01-25
Category : Computers
ISBN : 9781439827369

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Combinatorial Scientific Computing by Uwe Naumann,Olaf Schenk Pdf

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

Author : D. Rose
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461586753

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Sparse Matrices and their Applications by D. Rose Pdf

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.

Author : Iain S. Duff,A. M. Erisman,John Ker Reid
Publisher : Oxford University Press, USA
Page : 368 pages
File Size : 40,9 Mb
Release : 1986
Category : Language Arts & Disciplines
ISBN : UOM:39015014362803

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Direct Methods for Sparse Matrices by Iain S. Duff,A. M. Erisman,John Ker Reid Pdf

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.

Author : S.A. Soman,S.A. Khaparde,Shubha Pandit
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461508236

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Computational Methods for Large Sparse Power Systems Analysis by S.A. Soman,S.A. Khaparde,Shubha Pandit Pdf

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.

Author : Dinesh P. Mehta,Sartaj Sahni
Publisher : Taylor & Francis
Page : 1120 pages
File Size : 48,6 Mb
Release : 2018-02-21
Category : Computers
ISBN : 9781498701884

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Handbook of Data Structures and Applications by Dinesh P. Mehta,Sartaj Sahni Pdf

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.

Author : Amos Fiat
Publisher : Springer Science & Business Media
Page : 807 pages
File Size : 50,6 Mb
Release : 2009-09-03
Category : Computers
ISBN : 9783642041273

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Algorithms - ESA 2009 by Amos Fiat Pdf

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.

Author : Michel Daydé,José M.L.M. Palma,Álvaro L.G.A. Couthino,Esther Pacitti,João Correia Lopes
Publisher : Springer
Page : 728 pages
File Size : 41,6 Mb
Release : 2007-05-30
Category : Computers
ISBN : 9783540713517

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High Performance Computing for Computational Science - VECPAR 2006 by Michel Daydé,José M.L.M. Palma,Álvaro L.G.A. Couthino,Esther Pacitti,João Correia Lopes Pdf

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.

Author : Renchang Dai,Guangyi Liu
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 45,9 Mb
Release : 2023-09-28
Category : Technology & Engineering
ISBN : 9781119903888

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Graph Database and Graph Computing for Power System Analysis by Renchang Dai,Guangyi Liu Pdf

Graph Database and Graph Computing for Power System Analysis Understand a new way to model power systems with this comprehensive and practical guide Graph databases have become one of the essential tools for managing large data systems. Their structure improves over traditional table-based relational databases in that it reconciles more closely to the inherent physics of a power system, enabling it to model the components and the network of a power system in an organic way. The authors’ pioneering research has demonstrated the effectiveness and the potential of graph data management and graph computing to transform power system analysis. Graph Database and Graph Computing for Power System Analysis presents a comprehensive and accessible introduction to this research and its emerging applications. Programs and applications conventionally modeled for traditional relational databases are reconceived here to incorporate graph computing. The result is a detailed guide which demonstrates the utility and flexibility of this cutting-edge technology. The book’s readers will also find: Design configurations for a graph-based program to solve linear equations, differential equations, optimization problems, and more Detailed demonstrations of graph-based topology analysis, state estimation, power flow analysis, security-constrained economic dispatch, automatic generation control, small-signal stability, transient stability, and other concepts, analysis, and applications An authorial team with decades of experience in software design and power systems analysis Graph Database and Graph Computing for Power System Analysis is essential for researchers and academics in power systems analysis and energy-related fields, as well as for advanced graduate students looking to understand this particular set of technologies.

Author : Leszek Gąsieniec,Frank Wolter
Publisher : Springer
Page : 318 pages
File Size : 50,5 Mb
Release : 2013-07-22
Category : Computers
ISBN : 9783642401640

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Fundamentals of Computation Theory by Leszek Gąsieniec,Frank Wolter Pdf

This book constitutes the refereed proceedings of the 19th International Symposium on Fundamentals of Computation Theory, FCT 2013, held in Liverpool, UK, in August 2013. The 29 papers (26 full papers and 3 invited papers) were carefully reviewed and selected from 58 submissions. The papers cover the following topics: algorithms, formal methods, and emerging fields.