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Author | : Christopher G. Small |
Publisher | : OUP Oxford |
Total Pages | : 324 |
Release | : 2003-10-02 |
Genre | : Mathematics |
ISBN | : 0191545090 |
Download Numerical Methods for Nonlinear Estimating Equations Book in PDF, ePub and Kindle
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 | : Christopher G. Small |
Publisher | : Oxford University Press |
Total Pages | : 330 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9780198506881 |
Download Numerical Methods for Nonlinear Estimating Equations Book in PDF, ePub and Kindle
Non linearity 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 likelihood's 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 modification 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.
Author | : British Computer Society. Numerical Analysis Specialist Group |
Publisher | : Gordon & Breach Publishing Group |
Total Pages | : 216 |
Release | : 1970 |
Genre | : Mathematics |
ISBN | : |
Download Numerical Methods for Nonlinear Algebraic Equations Book in PDF, ePub and Kindle
Author | : J. E. Dennis, Jr. |
Publisher | : SIAM |
Total Pages | : 394 |
Release | : 1996-12-01 |
Genre | : Mathematics |
ISBN | : 9781611971200 |
Download Numerical Methods for Unconstrained Optimization and Nonlinear Equations Book in PDF, ePub and Kindle
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 |
Total Pages | : 394 |
Release | : 2015-01-19 |
Genre | : Mathematics |
ISBN | : 3319137972 |
Download Numerical Methods for Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
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 |
Publisher | : |
Total Pages | : 440 |
Release | : 1973 |
Genre | : Mathematics |
ISBN | : |
Download Numerical Solution of Systems of Nonlinear Algebraic Equations Book in PDF, ePub and Kindle
Author | : David Royce Sadler |
Publisher | : |
Total Pages | : 140 |
Release | : 1975 |
Genre | : Regression analysis |
ISBN | : |
Download Numerical Methods for Nonlinear Regression Book in PDF, ePub and Kindle
Author | : Ioannis K. Argyros |
Publisher | : CRC Press |
Total Pages | : 476 |
Release | : 2012-06-05 |
Genre | : Mathematics |
ISBN | : 1578087538 |
Download Numerical Methods for Equations and its Applications Book in PDF, ePub and Kindle
This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.
Author | : G. Alefeld |
Publisher | : Springer Science & Business Media |
Total Pages | : 253 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3709162173 |
Download Topics in Numerical Analysis Book in PDF, ePub and Kindle
This volume contains eighteen papers submitted in celebration of the sixty-fifth birthday of Professor Tetsuro Yamamoto of Ehime University. Professor Yamamoto was born in Tottori, Japan on January 4, 1937. He obtained his B. S. and M. S. in mathematics from Hiroshima University in 1959 and 1961, respec tively. In 1966, he took a lecturer position in the Department of Mathematics, Faculty of General Education, Hiroshima University and obtained his Ph. D. degree from Hiroshima University two years later. In 1969, he moved to the Department of Applied Mathematics, Faculty of Engineering, Ehime University as an associate professor and he has been a full professor of the Department of Mathematics (now Department of Mathematical Sciences), Faculty of Science, since 1975. At the early stage of his study, he was interested in algebraic eigen value problems and linear iterative methods. He published some papers on these topics in high level international journals. After moving to Ehime University, he started his research on Newton's method and Newton-like methods for nonlinear operator equations. He published many papers on error estimates of the methods. He established the remarkable result that all the known error bounds for Newton's method under the Kantorovich assumptions follow from the Newton-Kantorovich theorem, which put a period to the race of finding sharper error bounds for Newton's method.
Author | : Juan R. Torregrosa |
Publisher | : MDPI |
Total Pages | : 494 |
Release | : 2019-12-06 |
Genre | : Mathematics |
ISBN | : 3039219405 |
Download Iterative Methods for Solving Nonlinear Equations and Systems Book in PDF, ePub and Kindle
Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.