Numerical Methods For Nonlinear Estimating Equations

Author : Christopher G. Small,Jinfang Wang
Publisher : OUP Oxford
Page : 324 pages
File Size : 43,5 Mb
Release : 2003-10-02
Category : Mathematics
ISBN : 9780191545092

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Numerical Methods for Nonlinear Estimating Equations by Christopher G. Small,Jinfang Wang Pdf

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,Jinfang Wang
Publisher : Oxford University Press
Page : 330 pages
File Size : 46,9 Mb
Release : 2003
Category : Mathematics
ISBN : 0198506880

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Numerical Methods for Nonlinear Estimating Equations by Christopher G. Small,Jinfang Wang Pdf

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 : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 41,7 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209

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Numerical Methods for Unconstrained Optimization and Nonlinear Equations by J. E. Dennis, Jr.,Robert B. Schnabel Pdf

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 : William M. McEneaney
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 52,5 Mb
Release : 2006
Category : Language Arts & Disciplines
ISBN : 0817635343

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Max-Plus Methods for Nonlinear Control and Estimation by William M. McEneaney Pdf

The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated Hamilton–Jacobi–Bellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches. Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.

Author : R. Glowinski
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 41,5 Mb
Release : 2008-01-22
Category : Mathematics
ISBN : 9783540775065

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Lectures on Numerical Methods for Non-Linear Variational Problems by R. Glowinski Pdf

When Herb Keller suggested, more than two years ago, that we update our lectures held at the Tata Institute of Fundamental Research in 1977, and then have it published in the collection Springer Series in Computational Physics, we thought, at first, that it would be an easy task. Actually, we realized very quickly that it would be more complicated than what it seemed at first glance, for several reasons: 1. The first version of Numerical Methods for Nonlinear Variational Problems was, in fact, part of a set of monographs on numerical mat- matics published, in a short span of time, by the Tata Institute of Fun- mental Research in its well-known series Lectures on Mathematics and Physics; as might be expected, the first version systematically used the material of the above monographs, this being particularly true for Lectures on the Finite Element Method by P. G. Ciarlet and Lectures on Optimization—Theory and Algorithms by J. Cea. This second version had to be more self-contained. This necessity led to some minor additions in Chapters I-IV of the original version, and to the introduction of a chapter (namely, Chapter Y of this book) on relaxation methods, since these methods play an important role in various parts of this book.

Author : British Computer Society. Numerical Analysis Specialist Group
Publisher : Gordon & Breach Publishing Group
Page : 216 pages
File Size : 52,5 Mb
Release : 1970
Category : Mathematics
ISBN : MINN:31951000477408C

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Numerical Methods for Nonlinear Algebraic Equations by British Computer Society. Numerical Analysis Specialist Group Pdf

Author : Werner C. Rheinbolt
Publisher : Wiley-Interscience
Page : 326 pages
File Size : 51,9 Mb
Release : 1986
Category : Mathematics
ISBN : UCAL:B4405940

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Numerical Analysis of Parameterized Nonlinear Equations by Werner C. Rheinbolt Pdf

One of the leading experts in the field discusses recent developments in the numerical analysis of nonlinear equations involving a finite number of parameters. Shows how these equations can be developed on a differential geometric basis. Topics include equilibrium manifolds, path-tracing on manifolds, aspects of computational stability analysis, discretization errors of parameterized equations, and computational error assessment and related questions.

Author : George D. Byrne,Charles A. Hall
Publisher : Unknown
Page : 442 pages
File Size : 48,8 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015009789275

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Numerical Solution of Systems of Nonlinear Algebraic Equations by George D. Byrne,Charles A. Hall Pdf

Author : David Royce Sadler
Publisher : Unknown
Page : 140 pages
File Size : 47,5 Mb
Release : 1975
Category : Regression analysis
ISBN : STANFORD:36105032714565

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Numerical Methods for Nonlinear Regression by David Royce Sadler Pdf

Author : C. T. Kelley
Publisher : SIAM
Page : 179 pages
File Size : 54,5 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 1611970946

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Iterative Methods for Linear and Nonlinear Equations by C. T. Kelley Pdf

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.

Author : A. Cuyt,L. Wuytack
Publisher : Elsevier
Page : 277 pages
File Size : 43,8 Mb
Release : 1987-03-01
Category : Mathematics
ISBN : 0080872476

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Nonlinear Methods in Numerical Analysis by A. Cuyt,L. Wuytack Pdf

While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.

Author : Christopher T. H. Baker,Chris Phillips
Publisher : Oxford University Press, USA
Page : 394 pages
File Size : 55,8 Mb
Release : 1981
Category : Language Arts & Disciplines
ISBN : STANFORD:36105031980076

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The Numerical Solution of Nonlinear Problems by Christopher T. H. Baker,Chris Phillips Pdf

Author : George D. Byrne,Charles A. Hall
Publisher : Elsevier
Page : 430 pages
File Size : 49,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269306

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Numerical Solution of Systems of Nonlinear Algebraic Equations by George D. Byrne,Charles A. Hall Pdf

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 : Germund Dahlquist,Åke Björck
Publisher : Courier Corporation
Page : 773 pages
File Size : 55,8 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486139463

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Numerical Methods by Germund Dahlquist,Åke Björck Pdf

"Substantial, detailed and rigorous . . . readers for whom the book is intended are admirably served." — MathSciNet (Mathematical Reviews on the Web), American Mathematical Society. Practical text strikes fine balance between students' requirements for theoretical treatment and needs of practitioners, with best methods for large- and small-scale computing. Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography.

Author : Eugene L. Allgower,Kurt Georg
Publisher : SIAM
Page : 409 pages
File Size : 55,7 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 9780898715446

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Introduction to Numerical Continuation Methods by Eugene L. Allgower,Kurt Georg Pdf

Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.