Practical Extrapolation Methods
Author: Avram Sidi
Publisher: Cambridge University Press
Published: 2003-06-05
Total Pages: 546
ISBN-13: 9780521661591
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Author: Avram Sidi
Publisher: Cambridge University Press
Published: 2003-06-05
Total Pages: 546
ISBN-13: 9780521661591
DOWNLOAD EBOOKTable of contents
Author: Zahari Zlatev
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2017-11-07
Total Pages: 310
ISBN-13: 3110533006
DOWNLOAD EBOOKScientists and engineers are mainly using Richardson extrapolation as a computational tool for increasing the accuracy of various numerical algorithms for the treatment of systems of ordinary and partial differential equations and for improving the computational efficiency of the solution process by the automatic variation of the time-stepsizes. A third issue, the stability of the computations, is very often the most important one and, therefore, it is the major topic studied in all chapters of this book. Clear explanations and many examples make this text an easy-to-follow handbook for applied mathematicians, physicists and engineers working with scientific models based on differential equations. Contents The basic properties of Richardson extrapolation Richardson extrapolation for explicit Runge-Kutta methods Linear multistep and predictor-corrector methods Richardson extrapolation for some implicit methods Richardson extrapolation for splitting techniques Richardson extrapolation for advection problems Richardson extrapolation for some other problems General conclusions
Author: C. Brezinski
Publisher: Elsevier
Published: 2013-10-24
Total Pages: 475
ISBN-13: 0080506224
DOWNLOAD EBOOKThis volume is a self-contained, exhaustive exposition of the extrapolation methods theory, and of the various algorithms and procedures for accelerating the convergence of scalar and vector sequences. Many subroutines (written in FORTRAN 77) with instructions for their use are provided on a floppy disk in order to demonstrate to those working with sequences the advantages of the use of extrapolation methods. Many numerical examples showing the effectiveness of the procedures and a consequent chapter on applications are also provided – including some never before published results and applications. Although intended for researchers in the field, and for those using extrapolation methods for solving particular problems, this volume also provides a valuable resource for graduate courses on the subject.
Author: Keith R. Solomon
Publisher: CRC Press
Published: 2008-05-23
Total Pages: 408
ISBN-13: 1420073923
DOWNLOAD EBOOKA wide-ranging compilation of techniques, Extrapolation Practice for Ecotoxicological Effect Characterization of Chemicals describes methods of extrapolation in the framework of ecological risk assessment. The book, informally known as EXPECT, identifies data needs and situations where these extrapolations can be most usefully applied, makin
Author: Louis A. Hageman
Publisher: Elsevier
Published: 2014-06-28
Total Pages: 409
ISBN-13: 1483294374
DOWNLOAD EBOOKApplied Iterative Methods
Author: Forman S. Acton
Publisher: American Mathematical Soc.
Published: 2020-07-31
Total Pages: 549
ISBN-13: 147045727X
DOWNLOAD EBOOKAuthor: Avram Sidi
Publisher: SIAM
Published: 2017-09-26
Total Pages: 421
ISBN-13: 161197495X
DOWNLOAD EBOOKAn important problem that arises in different disciplines of science and engineering is that of computing limits of sequences of vectors of very large dimension. Such sequences arise, for example, in the numerical solution of systems of linear and nonlinear equations by fixed-point iterative methods, and their limits are simply the required solutions to these systems. The convergence of these sequences, which is very slow in many cases, can be accelerated successfully by using suitable vector extrapolation methods. Vector Extrapolation Methods with Applications?is the first book fully dedicated to the subject of vector extrapolation methods. It is a self-contained, up-to-date, and state-of-the-art reference on the theory and practice of the most useful methods. It covers all aspects of the subject, including development of the methods, their convergence study, numerically stable algorithms for their implementation, and their various applications. It also provides complete proofs in most places. As an interesting application, the author shows how these methods give rise to rational approximation procedures for vector-valued functions in the complex plane, a subject of importance in model reduction problems among others. This book is intended for numerical analysts, applied mathematicians, and computational scientists and engineers in fields such as computational fluid dynamics, structures, and mechanical and electrical engineering, to name a few. Since it provides complete proofs in most places, it can also serve as a textbook in courses on acceleration of convergence of iterative vector processes, for example.
Author: J. Stoer
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 674
ISBN-13: 1475722729
DOWNLOAD EBOOKOn the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.
Author: Rob J Hyndman
Publisher: OTexts
Published: 2018-05-08
Total Pages: 380
ISBN-13: 0987507117
DOWNLOAD EBOOKForecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.
Author: Lloyd N. Trefethen
Publisher: SIAM
Published: 2019-01-01
Total Pages: 377
ISBN-13: 1611975948
DOWNLOAD EBOOKThis is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.