Search results for: numerical-derivatives-and-nonlinear-analysis

Numerical Derivatives and Nonlinear Analysis

Author : Harriet Kagiwada
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For many years it has been an article of faith of numerical analysts that the evaluation of derivatives of complicated functions should be avoided. Derivatives were evaluated using finite differences or, more recently, using symbolic manipulation packages. The first has the disadvantage of limited accuracy. The second has disadvantages of being expensive and requiring considerable computer memory. The recent developments described in this text allow the evaluation of derivatives using simple automatic derivative evaluation subroutines pro grammed in FORTRAN or BASIC. These subroutines can even be programmed on a personal computer. The concept for the evaluation of the derivatives was originally developed by Wengert over 20 years ago. Significant im provements have been made in Wengert's method and are utilized in this text. The purpose of this text is to familiarize computer users with a simple and practical method for obtaining the partial derivatives of complicated mathematical expressions. The text illustrates the use of automatic deriva tive evaluation subroutines to solve a wide range of nonlinear least-squares, optimal control, system identification, two-point boundary value problems, and integral equations. The numerical values of the derivatives are evalu~ ated exactly, except for roundoff, using simple FORTRAN or BASIC sub routines. These derivatives are derived automatically behind the scenes, from the equivalent of analytical expressions, without any effort from the user. The use of costly software packages is not required.

Nonlinear Regression Analysis and Its Applications

Author : Douglas M Bates
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Wiley-Interscience Paperback Series The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The authors have put together an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models . . . highly recommend[ed] . . . for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." —Technometrics "[This book] provides a good balance of relevant theory and application with many examples . . . [and it] provides the most balanced approach to theory and application appropriate for a first course in nonlinear regression modeling for graduate statistics students." —Mathematical Reviews "[This book] joins a distinguished list of publications with a reputation for balancing technical rigor with readability, and theory with application. [It] upholds tradition . . . [and is] a worthwhile reference for the marketing researcher with a serious interest in linear models." —Journal of Marketing Research This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares. The authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. The book also includes pseudocode for computing algorithms.

Computation in Economics Finance and Engineering

Author : Sean Holly
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This volume contains papers that were presented at the Symposium on Computation in Economics and Finance organised under the auspices of the International Federation of Automatic Control and the Society for Computational Economics. The Conference was held at Cambridge University, UK, from 29th June to the 1st July 1998. It attracted many members of the international academic and research community in computational economics, finance and econometrics. This volume brings together a number of papers that demonstrate the use of computational methods in a variety of areas in economics and finance. The contributions to the Symposium reflect the various shifts in the profession and the increasing use of computationally intensive techniques for the analysis of economic processes. Papers have been grouped into sections, according to their context rather than in the order in which they were presented. Section 1 groups papers in the area of Finance including both theoretical and empirical studies. Section 2 reflects a fast growing interest in seeking to model economic processes in novel ways drawing on the emerging literature in artificial intelligence and genetic adaptation. Section 3 demonstrates the growing use of computational languages as a tool for the analysis and modelling of economic systems. Subsequent sections range across many areas involving game theory, policy co-ordination, agent based models, time series and econometrics, neural networks, nonlinearities and simulation methods. The preparation and selection of this volume owes much to the assistance and advice of both Berç Rustem and David Kendrick and the steering committee of the Society for Computational Economics.

The Bulletin of Mathematics Books

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Economic Report Series

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Choice

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Applied Identification Modelling and Simulation AIMS 84

Author : International Association of Science and Technology for Development
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Numerical Procedures for Analysis of Structural Shells

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An evaluation is undertaken of currently used discretization procedures in numerical analysis of structures. Emphasis is on the nonlinear behavior of thin shells and plates. It is found that the computer economy is extremely sensitive to the choice of element configuration. A proper balance between the order of the approximations of inplane and lateral displacements is important. The best finite element procedures are superior to finite differences for bifurcation buckling and for moderate nonlinearity. However, for shell collapse analysis the finite differences approach is quite superior to the finite elements. Suggestions are made for improvement of finite element technology for structures undergoing large rotations.

Mathematical Reviews

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Nonlinear Analysis in Chemical Engineering

Author : Bruce A. Finlayson
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Scientific Computation and Differential Equations

Author : Christopher T. H. Baker
File Size : 45.14 MB
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Proceedings -- Computer Arithmetic, Algebra, OOP.

OOPSLA 89 Conference Proceedings

Author : Norman Meyrowitz
File Size : 52.13 MB
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Explorations In Numerical Analysis

Author : James V Lambers
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This textbook introduces advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include error analysis, computer arithmetic, solution of systems of linear equations, least squares problems, eigenvalue problems, polynomial interpolation and approximation, numerical differentiation and integration, nonlinear equations, optimization, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the MATLAB programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

Reliability in Computing

Author : Ramon E. Moore
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Mathematics of Computing -- Numerical Analysis.

Using R for Numerical Analysis in Science and Engineering

Author : Victor A. Bloomfield
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Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also: Explains how to statistically analyze and fit data to linear and nonlinear models Explores numerical differentiation, integration, and optimization Describes how to find eigenvalues and eigenfunctions Discusses interpolation and curve fitting Considers the analysis of time series Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R.

Mathematical Programming

Author : Masao Iri
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Numerical Methods for Nonlinear Engineering Models

Author : John R. Hauser
File Size : 49.30 MB
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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.

International Mathematical News

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Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.

Real and Functional Analysis

Author : Arunava Mukherjea
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MSC NASTRAN Handbook for Nonlinear Analysis

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