Direct Methods for Sparse Matrices

Author: I. S. Duff,A. M. Erisman,J. K. Reid
Publisher: Oxford University Press
ISBN: 0192507508
Category: Mathematics
Page: 416
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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.

Computer Algebra in Scientific Computing

18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings
Author: Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher: Springer
ISBN: 3319456415
Category: Computers
Page: 513
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This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.

Transactions on Large-Scale Data- and Knowledge-Centered Systems VII

Author: Abdelkader Hameurlain,Josef Küng,Roland Wagner
Publisher: Springer
ISBN: 3642353320
Category: Computers
Page: 171
View: 7803

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The LNCS journal Transactions on Large-Scale Data- and Knowledge-Centered Systems focuses on data management, knowledge discovery, and knowledge processing, which are core and hot topics in computer science. Since the 1990s, the Internet has become the main driving force behind application development in all domains. An increase in the demand for resource sharing across different sites connected through networks has led to an evolution of data- and knowledge-management systems from centralized systems to decentralized systems enabling large-scale distributed applications providing high scalability. Current decentralized systems still focus on data and knowledge as their main resource. Feasibility of these systems relies basically on P2P (peer-to-peer) techniques and the support of agent systems with scaling and decentralized control. Synergy between grids, P2P systems, and agent technologies is the key to data- and knowledge-centered systems in large-scale environments. This, the seventh issue of Transactions on Large-Scale Data- and Knowledge-Centered Systems, contains five revised selected regular papers on the following topics: data management, data streams, service-oriented computing, abstract algebraic frameworks, RDF and ontologies, and conceptual model frameworks.

Direct methods for sparse matrices

Author: Iain S. Duff,A. M. Erisman,John Ker Reid
Publisher: Oxford University Press, USA
Category: Mathematics
Page: 341
View: 9592

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This book provides practical approaches to the efficient use of sparsity--a key to solving large problems in many fields, including computational science and engineering, where mathematical models give rise to very large systems of linear equations. The emphasis is on practicality, with conclusions based on concrete experience. Non-numeric computing techniques have been included as well as frequent illustrations in an attempt to bridge the gap between the written word and the working computer code. Exercises have been included to strengthen understanding of the material as well as to extend it for students and researchers in engineering, mathematics, and computer science.

Computational Methods for General Sparse Matrices

Author: Zahari Zlatev
Publisher: Springer Science & Business Media
ISBN: 940171116X
Category: Computers
Page: 328
View: 835

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'Et moi ... - si j'avait su comment en revenir, One service mathematics has rendered the je n 'y serais point aile.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.

Computational Methods for Large Sparse Power Systems Analysis

An Object Oriented Approach
Author: S. A. Soman,S. A. Khaparde,Shubha Pandit
Publisher: Springer Science & Business Media
ISBN: 9780792375913
Category: Computers
Page: 333
View: 330

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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.

Direct Methods for Sparse Linear Systems

Author: Timothy A. Davis
Publisher: SIAM
ISBN: 0898716136
Category: Computers
Page: 217
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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.

High-Performance Scientific Computing

Algorithms and Applications
Author: Michael W. Berry,Kyle A. Gallivan,Efstratios Gallopoulos,Ananth Grama,Bernard Philippe,Yousef Saad,Faisal Saied
Publisher: Springer Science & Business Media
ISBN: 1447124367
Category: Computers
Page: 350
View: 8197

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This book presents the state of the art in parallel numerical algorithms, applications, architectures, and system software. The book examines various solutions for issues of concurrency, scale, energy efficiency, and programmability, which are discussed in the context of a diverse range of applications. Features: includes contributions from an international selection of world-class authorities; examines parallel algorithm-architecture interaction through issues of computational capacity-based codesign and automatic restructuring of programs using compilation techniques; reviews emerging applications of numerical methods in information retrieval and data mining; discusses the latest issues in dense and sparse matrix computations for modern high-performance systems, multicores, manycores and GPUs, and several perspectives on the Spike family of algorithms for solving linear systems; presents outstanding challenges and developing technologies, and puts these in their historical context.

Large-Scale Scientific Computing

Third International Conference, LSSC 2001, Sozopol, Bulgaria, June 6-10, 2001. Revised Papers
Author: Svetozar Margenov,LSSC,Jerzy Wasniewski
Publisher: Springer Science & Business Media
ISBN: 3540430431
Category: Computers
Page: 498
View: 7398

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Thepurposeoftheconferencewastobringtogetherscientistsworkingwith largecomputationalproblemsinindustry,andspecialistsinthe?eldofnume- calanalysis‘methodsande?cientexploitationofmodernhigh-speedcomputers. Someclassesofmethodsappearagainandagaininthenumericaltreatmentof problemsfromdi?erent?eldsofscienceandengineering. Theaimofthisconf- encewastoselectsomeofthesenumericalmethodsandplanfurtherexperiments onseveraltypesofparallelcomputers. Thekeylecturesreviewedthemostimp- tantnumericalalgorithmsandscienti?capplicationsonparallelcomputers. The invited speakers included university and practical engineers from industry, as wellasappliedmathematicians,numericalanalysts,andcomputerexperts.

Data-Driven Modeling & Scientific Computation

Methods for Complex Systems & Big Data
Author: J. Nathan Kutz
Publisher: OUP Oxford
ISBN: 019163588X
Category: Language Arts & Disciplines
Page: 608
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The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: · statistics, · time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems. Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

Mathematical Physics and Stochastic Analysis

Essays in Honour of Ludwig Streit
Author: Sergio Albeverio
Publisher: World Scientific
ISBN: 9789810244408
Category: Science
Page: 438
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In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality.The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains.List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Boll‚, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M R”ckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L V zquez, D N Kozakevich, S Jim‚nez, V R Vieira, P D Sacramento, R Vilela Mendes, D Voln?, P Samek.

Numerical Methods in Matrix Computations

Author: Åke Björck
Publisher: Springer
ISBN: 3319050893
Category: Mathematics
Page: 800
View: 2126

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Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

IUTAM Symposium on Computational Methods for Unbounded Domains

Author: Thomas L. Geers
Publisher: Springer Science & Business Media
ISBN: 9780792352662
Category: Technology & Engineering
Page: 328
View: 2932

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This volume constitutes the proceedings of the 1997 IUTAM Symposium, where invited researchers in acoustics, aeronautics, elastodynamics, electromagnetics, hydrodynamics, and mathematics discussed non-reflecting computational boundaries. The participants formulated benchmark problems for evaluating computational boundaries, as described in the first article.

Numerical Mathematics and Advanced Applications

Proceedings of ENUMATH 2005 the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005
Author: Alfredo Bermúdez de Castro,Dolores Gómez,Peregrina Quintela,Pilar Salgado
Publisher: Springer Science & Business Media
ISBN: 3540342885
Category: Mathematics
Page: 1232
View: 1837

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These proceedings collect lectures given at ENUMATH 2005, the 6th European Conference on Numerical Mathematics and Advanced Applications held in Santiago de Compostela, Spain in July, 2005. Topics include applications such as fluid dynamics, electromagnetism, structural mechanics, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, and more.

Numerical Methods and Applications

5th International Conference, NMA 2002, Borovets, Bulgaria, August 20-24, 2002, Revised Papers
Author: Ivan Dimov,Ivan Lirkov,Svetozar Margenov,Zahari Zlatev
Publisher: Springer Science & Business Media
ISBN: 3540006087
Category: Computers
Page: 574
View: 5861

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Nuclear magnetic resonance spectroscopy is one of the most important analytical methods available today. This practice-oriented textbook aims at teaching the use of NMR spectra in the elucidation of organic structures. The emphasis of NMR - from Spectra to Structures is on practical rather than on theoretical aspects, which are treated only briefly. The book is intended as a practical guide to today's standard NMR experiments for students and laboratory personnel. A set of thirty-five graded problems reinforces the reader's understanding of how problems of structure elucidation are solved by using NMR.