Direct Methods for Sparse Linear Systems

Author: Timothy A. Davis

Publisher: SIAM

ISBN: 9780898718881

Category: Linear systems

Page: 217

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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.

Sparse Matrix Technology

Author: Sergio Pissanetzky

Publisher: Academic Press

ISBN: 1483270408

Category: Mathematics

Page: 336

View: 4528

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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.

Solving Nonlinear Equations with Newton's Method

Author: C. T. Kelley

Publisher: SIAM

ISBN: 9780898718898

Category: Iterative methods (Mathematics)

Page: 104

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This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.

Numerical Methods in Matrix Computations

Author: Åke Björck

Publisher: Springer

ISBN: 3319050893

Category: Mathematics

Page: 800

View: 5931

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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.

Iterative Methods for Linear and Nonlinear Equations

Author: C. T. Kelley

Publisher: SIAM

ISBN: 9781611970944

Category: Iterative methods (Mathematics)

Page: 166

View: 9449

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Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

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: 1642

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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.


Author: Kermit Sigmon,Timothy A. Davis

Publisher: CRC Press

ISBN: 9781420034950

Category: Mathematics

Page: 232

View: 2327

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With the spread of the powerhouse MATLAB® software into nearly every area of math, science, and engineering, it is important to have a strong introduction to using the software. Updated for version 7.0, MATLAB® Primer, Seventh Edition offers such an introduction as well as a "pocketbook" reference for everyday users of the software. It offers an intuitive language for expressing problems and solutions both numerically and graphically. The latest edition in this best-selling series, MATLAB® Primer, Seventh Edition incorporates a number of enhancements such as changes to the desktop, new features for developing M-files, the JIT accelerator, and an easier way of importing Java classes. In addition to the features new to version 7.0, this book includes: A new section on M-Lint, the new debugger for M-files A new chapter on calling Java from MATLAB and using Java objects inside the MATLAB workspace A new chapter on calling Fortran from MATLAB A new chapter on solving equations: symbolic and numeric polynomials, nonlinear equations, and differential equations A new chapter on cell publishing, which replaces the "notebook" feature and allows the creation of Word, LaTeX, PowerPoint, and HTML documents with executable MATLAB commands and their outputs Expanded Graphics coverage-including the 3D parametrically defined seashells on the front and back covers Whether you are new to MATLAB, new to version 7.0, or simply in need of a hands-on, to-the-point reference, MATLAB® Primer provides the tools you need in a conveniently sized, economically priced pocketbook.

Numerical Methods for Large Eigenvalue Problems

Revised Edition

Author: Yousef Saad

Publisher: SIAM

ISBN: 9781611970739

Category: Eigenvalues

Page: 276

View: 353

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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.

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

View: 4700

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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.

Applied Numerical Linear Algebra

Author: James W. Demmel

Publisher: SIAM

ISBN: 0898713897

Category: Mathematics

Page: 419

View: 2132

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This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Introduction to Algorithms

Author: Thomas H. Cormen

Publisher: MIT Press

ISBN: 0262533057

Category: Computers

Page: 1292

View: 3865

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A new edition of the essential text and professional reference, with substantial new material on such topics as vEB trees, multithreaded algorithms, dynamic programming, and edge-based flow.

Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications

Author: Daniele Bertaccini,Fabio Durastante

Publisher: CRC Press

ISBN: 1351649612

Category: Mathematics

Page: 354

View: 3559

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This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.

Iterative Methods for Optimization

Author: C. T. Kelley

Publisher: SIAM

ISBN: 9781611970920

Category: Iterative methods (Mathematics)

Page: 180

View: 5476

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This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.

Numerical Linear Algebra

Author: Lloyd N. Trefethen,David Bau, III

Publisher: SIAM

ISBN: 9780898719574

Category: Algebras, Linear

Page: 361

View: 9417

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A concise, insightful, and elegant introduction to the field of numerical linear algebra. Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic, it has already been class-tested by MIT and Cornell graduate students from all fields of mathematics, engineering, and the physical sciences. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike.

Sensitivity Analysis in Linear Systems

Author: Assem Deif

Publisher: Springer Science & Business Media

ISBN: 364282739X

Category: Mathematics

Page: 224

View: 8567

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A text surveying perturbation techniques and sensitivity analysis of linear systems is an ambitious undertaking, considering the lack of basic comprehensive texts on the subject. A wide-ranging and global coverage of the topic is as yet missing, despite the existence of numerous monographs dealing with specific topics but generally of use to only a narrow category of people. In fact, most works approach this subject from the numerical analysis point of view. Indeed, researchers in this field have been most concerned with this topic, although engineers and scholars in all fields may find it equally interesting. One can state, without great exaggeration, that a great deal of engineering work is devoted to testing systems' sensitivity to changes in design parameters. As a rule, high-sensitivity elements are those which should be designed with utmost care. On the other hand, as the mathematical modelling serving for the design process is usually idealized and often inaccurately formulated, some unforeseen alterations may cause the system to behave in a slightly different manner. Sensitivity analysis can help the engineer innovate ways to minimize such system discrepancy, since it starts from the assumption of such a discrepancy between the ideal and the actual system.

An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation

Author: Victorita Dolean,Pierre Jolivet,Frâdâric Nataf

Publisher: SIAM

ISBN: 1611974054

Category: Science

Page: 238

View: 4839

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The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.÷