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Author : E.L. Allgöwer,K. Glashoff,H.-O. Peitgen
Publisher : Springer
Page : 457 pages
File Size : 47,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387817
Author : George D. Byrne,Charles A. Hall
Publisher : Unknown
Page : 442 pages
File Size : 42,9 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015009789275
Author : John R. Hauser
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 53,5 Mb
Release : 2009-03-24
Category : Technology & Engineering
ISBN : 9781402099205
There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.
Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 52,5 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author : Sören Bartels
Publisher : Springer
Page : 393 pages
File Size : 48,7 Mb
Release : 2015-01-19
Category : Mathematics
ISBN : 9783319137971
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Author : George D. Byrne,Charles A. Hall
Publisher : Elsevier
Page : 430 pages
File Size : 45,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269306
Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July 10-14, 1972. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics. The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. These topics are followed by a survey of some computational techniques for the nonlinear least squares problem. The remaining chapters explore the problem of nonlinear functional minimization, the modification methods, and the computer-oriented algorithms for solving system. These chapters also examine the principles of contractor theory of solving equations. This book will prove useful to undergraduate and graduate students.
Author : British Computer Society. Numerical Analysis Specialist Group
Publisher : Gordon & Breach Publishing Group
Page : 216 pages
File Size : 54,7 Mb
Release : 1970
Category : Mathematics
ISBN : MINN:31951000477408C
Author : C. T. Kelley
Publisher : SIAM
Page : 117 pages
File Size : 50,7 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718899
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.
Author : E. L. Allgower,K. Glashoff,Heinz-Otto Peitgen
Publisher : Unknown
Page : 128 pages
File Size : 44,7 Mb
Release : 1981
Category : Electronic
ISBN : OCLC:476335578
Author : Christopher T. H. Baker,Chris Phillips
Publisher : Oxford University Press, USA
Page : 392 pages
File Size : 42,5 Mb
Release : 1981
Category : Boundary value problems
ISBN : UCAL:B4980150
Author : Inna Shingareva,Carlos Lizárraga-Celaya
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 44,7 Mb
Release : 2011-07-24
Category : Mathematics
ISBN : 9783709105177
The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).
Author : Christopher G. Small,Jinfang Wang
Publisher : OUP Oxford
Page : 324 pages
File Size : 52,6 Mb
Release : 2003-10-02
Category : Mathematics
ISBN : 9780191545092
Nonlinearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which, when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modifications to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student. This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specifically original. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user's perspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjort & Sylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction
Author : Anonim
Publisher : Unknown
Page : 22 pages
File Size : 49,7 Mb
Release : 1993
Category : GAUSS (Computer program)
ISBN : OCLC:965390892
Solves systems of nonlinear equations having as many equations as unknowns.
Author : Sujaul Chowdhury,Syed Badiuzzaman Faruque,Ponkog Kumar Das
Publisher : CRC Press
Page : 77 pages
File Size : 44,9 Mb
Release : 2021-10-25
Category : Mathematics
ISBN : 9781000486148
The book presents in comprehensive detail numerical solutions to boundary value problems of a number of non-linear differential equations. Replacing derivatives by finite difference approximations in these differential equations leads to a system of non-linear algebraic equations which we have solved using Newton’s iterative method. In each case, we have also obtained Euler solutions and ascertained that the iterations converge to Euler solutions. We find that, except for the boundary values, initial values of the 1st iteration need not be anything close to the final convergent values of the numerical solution. Programs in Mathematica 6.0 were written to obtain the numerical solutions.
Author : J. M. Ortega,W. C. Rheinboldt
Publisher : Elsevier
Page : 592 pages
File Size : 46,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483276724
Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.