Computer Solution of Large Linear Systems

Author: Gerard Meurant

Publisher: Elsevier

ISBN: 9780080529516

Category: Mathematics

Page: 776

View: 2929

This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

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: 1461508231

Category: Technology & Engineering

Page: 335

View: 2836

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.

High Performance Computing Systems and Applications

Author: Jonathan Schaeffer

Publisher: Springer Science & Business Media

ISBN: 1461556112

Category: Computers

Page: 464

View: 9900

Major advances in computing are occurring at an ever-increasing pace. This is especially so in the area of high performance computing (HPC), where today's supercomputer is tomorrow's workstation. High Performance Computing Systems and Applications is a record of HPCS'98, the 12th annual Symposium on High Performance Computing Systems and Applications. The quality of the conference was significantly enhanced by the high proportion of keynote and invited speakers. This book presents the latest research in HPC architecture, networking, applications and tools. Of special note are the sections on computational biology and physics. High Performance Computing Systems and Applications is suitable as a secondary text for a graduate-level course on computer architecture and networking, and as a reference for researchers and practitioners in industry.

Iterative Solution of Large Sparse Systems of Equations

Author: Wolfgang Hackbusch

Publisher: Springer

ISBN: 3319284835

Category: Mathematics

Page: 509

View: 8683

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

Finite Elements, Electromagnetics and Design

Author: S.R.H. Hoole

Publisher: Elsevier

ISBN: 0080531687

Category: Technology & Engineering

Page: 468

View: 4903

Advanced topics of research in field computation are explored in this publication. Contributions have been sourced from international experts, ensuring a comprehensive specialist perspective. A unity of style has been achieved by the editor, who has specifically inserted appropriate cross-references throughout the volume, plus a single collected set of references at the end. The book provides a multi-faceted overview of the power and effectiveness of computation techniques in engineering electromagnetics. In addition to examining recent and current developments, it is hoped that it will stimulate further research in the field.

Direct Methods for Sparse Linear Systems

Author: Timothy A. Davis

Publisher: SIAM

ISBN: 0898716136

Category: Computers

Page: 217

View: 2242

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.

Templates for the Solution of Linear Systems

Building Blocks for Iterative Methods

Author: Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst

Publisher: SIAM

ISBN: 9781611971538

Category: Mathematics

Page: 112

View: 5171

In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides "value-added" capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful.

Laser Spectroscopy IV

Proceedings of the Fourth International Conference, Rottarch-Egern, Fed. Rep. of Germany, June 11-15, 1979

Author: Herbert Walther,K. W. Rothe

Publisher: Springer Science & Business Media

ISBN: 038709766X

Category: Computers

Page: 652

View: 866

Traditionally, the discipline of parallel computing has encompassed a wide range of topics ranging from machine organization all the way to applications. The Encyclopedia of Parallel Computing is likewise broad in scope, covering machine organization, programming, algorithms, and applications. Within each area, the Encyclopedia covers concepts, designs, and specific implementations. In the area of algorithms, the encyclopedia will cover (1) concepts such as cache-oblivious algorithms and systolic algorithms, (2) specific numerical and non-numerical algorithms such as parallel matrix-matrix multiplication and graph algorithms to, for example, find connected components in parallel, and (3) implementations of algorithms in the form of widely used libraries such as LAPACK. In the area of architecture, the encyclopedia will contain (1) concepts such as sequential consistency and cache coherency, (2) machine classes such as shared-memory multiprocessors and dataflow machines, and (3) specific machines such as IBM's cell processor and Intel's multicore machines. In the area of software, it will cover (1) concepts such as races and autoparallelization, and (2) designs in the form of parallel programming languages, library interfaces, and operating systems. The encyclopedia also will cover application issues emphasizing the type of parallel computation involved and the magnitude in terms of computational requirements of the applications.Each encyclopedia entry will be concise and clear and will contain references to the literature for readers wishing to study the topic of the entry in depth. The broad coverage--together with extensive pointers to the literature for in-depth study'will make the encyclopedia an invaluable reference tool for researchers, practitioners and students alike.

Sparse Matrix Technology

Author: Sergio Pissanetzky

Publisher: Academic Press

ISBN: 1483270408

Category: Mathematics

Page: 336

View: 3543

Sparse Matrix Technology presents the methods, concepts, ideas, and applications of sparse matrix technology. The text provides the fundamental methods, procedures, techniques, and applications of sparse matrix technology in software development. The book covers topics on storage schemes and computational techniques needed for sparse matrix technology; sparse matrix methods and algorithms for the direct solution of linear equations; and algorithms for different purposes connected with sparse matrix technology. Engineers, programmers, analysts, teachers, and students in the computer sciences will find the book interesting.

Adjustment Computations

Spatial Data Analysis

Author: Charles D. Ghilani

Publisher: John Wiley & Sons

ISBN: 1118174402

Category: Technology & Engineering

Page: 672

View: 1847

the complete guide to adjusting for measurement error—expanded and updated no measurement is ever exact. Adjustment Computations updates a classic, definitive text on surveying with the latest methodologies and tools for analyzing and adjusting errors with a focus on least squares adjustments, the most rigorous methodology available and the one on which accuracy standards for surveys are based. This extensively updated Fifth Edition shares new information on advances in modern software and GNSS-acquired data. Expanded sections offer a greater amount of computable problems and their worked solutions, while new screenshots guide readers through the exercises. Continuing its legacy as a reliable primer, Adjustment Computations covers the basic terms and fundamentals of errors and methods of analyzing them and progresses to specific adjustment computations and spatial information analysis. Current and comprehensive, the book features: Easy-to-understand language and an emphasis on real-world applications Analyzing data in three dimensions, confidence intervals, statistical testing, and more An updated support web page containing a 150-page solutions manual, software (STATS, ADJUST, and MATRIX for Windows computers), MathCAD worksheets, and more at The latest information on advanced topics such as the tau criterion used in post-adjustment statistical blunder detection Adjustment Computations, Fifth Edition is an invaluable reference and self-study resource for working surveyors, photogrammetrists, and professionals who use GNSS and GIS for data collection and analysis, including oceanographers, urban planners, foresters, geographers, and transportation planners. It's also an indispensable resource for students preparing for licensing exams and the ideal textbook for courses in surveying, civil engineering, forestry, cartography, and geology.

Iterative Solution of Large Linear Systems

Author: David M. Young

Publisher: Elsevier

ISBN: 1483274136

Category: Mathematics

Page: 598

View: 6706

Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.

Sparse Matrix Techniques

Copenhagen 1976

Author: V.A. Barker

Publisher: Springer

ISBN: 3540374302

Category: Mathematics

Page: 187

View: 5720

PLTMG, a Software Package for Solving Elliptic Partial Differential Equations

Users' Guide 8.0

Author: Randolph E. Bank

Publisher: SIAM

ISBN: 9780898719635

Category: Differential equations, Elliptic

Page: 110

View: 3867

Intended mainly for use as a reference manual, this edition encompasses all the improvements of the newest version of the PLTMG software package. This updated version introduces several significant changes.


Living in the Crossfire

Author: Alan George

Publisher: Zed Books Ltd.

ISBN: 184813715X

Category: Political Science

Page: 288

View: 7849

Jordan has played a bigger role in Middle Eastern affairs than its size and economy might warrant, due to its huge Palestinian population, its strategic location between Israel, the West Bank, Syria and Iraq, and its uniquely close relationship with successive British and US administrations. Drawing on numerous visits to the country and interviews with a diversity of people from King Abdullah down, Alan George describes how its reasonably stable monarchical system, unlike that in most Arab countries, has allowed the halting development of civil society and maintained control through the skilful co-option of opponents rather than heavy-handed reliance on its secret police. What is daily life like? How do its parliamentary system and political parties work? How free are the media? What are the future prospects of this buffer 'state without a nation'?

Iterative Methods for Large Linear Systems

Author: David R. Kincaid,Linda J. Hayes

Publisher: Academic Press

ISBN: 1483260208

Category: Mathematics

Page: 350

View: 9417

Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.


Tools for Science and Technology

Author: Stéphane Jaffard,Yves Meyer,Robert Dean Ryan

Publisher: SIAM

ISBN: 9780898718119

Category: Wavelets (Mathematics)

Page: 256

View: 2578

This long-awaited update of Meyer's Wavelets : algorithms and applications includes completely new chapters on four topics: wavelets and the study of turbulence, wavelets and fractals (which includes an analysis of Riemann's nondifferentiable function), data compression, and wavelets in astronomy. The chapter on data compression was the original motivation for this revised edition, and it contains up-to-date information on the interplay between wavelets and nonlinear approximation. The other chapters have been rewritten with comments, references, historical notes, and new material. Four appendices have been added: a primer on filters, key results (with proofs) about the wavelet transform, a complete discussion of a counterexample to the Marr-Mallat conjecture on zero-crossings, and a brief introduction to Hölder and Besov spaces. In addition, all of the figures have been redrawn, and the references have been expanded to a comprehensive list of over 260 entries. The book includes several new results that have not appeared elsewhere.