Direct Methods for Sparse Matrices

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Author: I. S. Duff,A. M. Erisman,J. K. Reid

Publisher: Oxford University Press

ISBN: 0192507508

Category: Mathematics

Page: 416

View: 3914

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.

Direct Methods for Sparse Linear Systems

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Author: Timothy A. Davis

Publisher: SIAM

ISBN: 0898716136

Category: Computers

Page: 217

View: 1226

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 Algebra in Scientific Computing

18th International Workshop, CASC 2016, Bucharest, Romania, September 19-23, 2016, Proceedings

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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.

Numerical Methods for Large Eigenvalue Problems

Revised Edition

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Author: Yousef Saad

Publisher: SIAM

ISBN: 9781611970739

Category: Eigenvalues

Page: 276

View: 5487

This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

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

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Author: Abdelkader Hameurlain,Josef Küng,Roland Wagner

Publisher: Springer

ISBN: 3642353320

Category: Computers

Page: 171

View: 4665

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.

Numerical Methods in Matrix Computations

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Author: Åke Björck

Publisher: Springer

ISBN: 3319050893

Category: Mathematics

Page: 800

View: 7072

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.

Sparse Matrix Computations

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Author: James R. Bunch,Donald J. Rose

Publisher: Academic Press

ISBN: 1483263401

Category: Mathematics

Page: 468

View: 4325

Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.

Modern Fortran Explained

Incorporating Fortran 2018

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Author: Michael Metcalf,John Reid,Malcolm Cohen

Publisher: Oxford University Press

ISBN: 0192539876

Category: Computers

Page: 543

View: 2847

Fortran marches on, remaining one of the principal programming languages used in high-performance scientific, numerical, and engineering computing. A series of significant revisions to the standard versions of the language have progressively enhanced its capabilities, and the latest standard - Fortran 2018 - includes many additions and improvements. This edition of Modern Fortran Explained expands on the last. Given the release of updated versions of Fortran compilers, the separate descriptions of Fortran 2003 and Fortran 2008 have been incorporated into the main text, which thereby becomes a unified description of the full Fortran 2008 version of the language. This clearer standard has allowed many deficiencies and irregularities in the earlier language versions to be resolved. Four new chapters describe the additional features of Fortran 2018, with its enhancements to coarrays for parallel programming, interoperability with C, IEEE arithmetic, and various other improvements. Written by leading experts in the field, two of whom have actively contributed to Fortran 2018, this is a complete and authoritative description of Fortran in its latest form. It is intended for new and existing users of the language, and for all those involved in scientific and numerical computing. It is suitable as a textbook for teaching and, with its index, as a handy reference for practitioners.

Numerical Methods for Least Squares Problems

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Author: Ake Björck

Publisher: SIAM

ISBN: 9781611971484

Category: Equations, Simultaneous

Page: 408

View: 6962

The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.

Scientific Computing with Case Studies

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Author: Dianne P. O'Leary

Publisher: SIAM

ISBN: 0898716667

Category: Mathematics

Page: 383

View: 1367

This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.

Accuracy and Stability of Numerical Algorithms

Second Edition

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Author: Nicholas J. Higham

Publisher: SIAM

ISBN: 9780898718027

Category: Computer algorithms

Page: 680

View: 777

Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Parallel Scientific Computing

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Author: Frédéric Magoules,Fran?ois-Xavier Roux,Guillaume Houzeaux

Publisher: John Wiley & Sons

ISBN: 1848215819

Category: Computers

Page: 372

View: 3077

"Scientific computing has become an indispensable tool in numerous fields, such as physics, biology, chemistry, finance and engineering. For example, it enables us, thanks to efficient algorithms adapted to current computers and supercomputers, to simulate complex phenomena, without the help of models or experimentations. Some examples are the structural behaviors of civil engineering structures, the sound level in a theater, a fluid flowing around an aircraft or a Formula 1 car, and the hydrodynamics of a racing yacht. This book presents the scientific computing techniques applied to parallel computing for the numerical simulation of large-scale problems ; these problems mainly result from systems modeled by partial differential equations. Computing concepts are tackled via examples. Implementation and programming techniques resulting from the finite element, finite volume and finite difference methods are presented for direct solvers, iterative solvers and domain decomposition methods, along with an introduction to MPI and OpenMP." (source : 4ème de couverture).

Scientific Computing and Differential Equations

An Introduction to Numerical Methods

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Author: Gene H. Golub,James M. Ortega

Publisher: Elsevier

ISBN: 0080516696

Category: Mathematics

Page: 344

View: 7715

Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level. An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment Contains an introduction to numerical methods for both ordinary and partial differential equations Concentrates on ordinary differential equations, especially boundary-value problems Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level

Computational Methods for Large Sparse Power Systems Analysis

An Object Oriented Approach

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Author: S. A. Soman,S. A. Khaparde,Shubha Pandit

Publisher: Springer Science & Business Media

ISBN: 9780792375913

Category: Computers

Page: 333

View: 4073

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.

Applied Iterative Methods

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Author: Louis A. Hageman

Publisher: Elsevier

ISBN: 1483294374

Category: Mathematics

Page: 386

View: 9993

Applied Iterative Methods

Numerical Analysis

Mathematics of Scientific Computing

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Author: David Ronald Kincaid,Elliott Ward Cheney

Publisher: American Mathematical Soc.

ISBN: 0821847880

Category: Mathematics

Page: 788

View: 3494

This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.

Numerical Linear Algebra with Applications

Using MATLAB

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Author: William Ford

Publisher: Academic Press

ISBN: 0123947847

Category: Mathematics

Page: 628

View: 4136

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra Detailed explanations and examples A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra Examples from engineering and science applications