Newton Methods For Nonlinear Problems
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Newton Methods For Nonlinear Problems
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Author : Peter Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-13
Newton Methods For Nonlinear Problems written by Peter Deuflhard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-13 with Mathematics categories.
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
Newton Methods For Nonlinear Problems
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Author : Peter Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-18
Newton Methods For Nonlinear Problems written by Peter Deuflhard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-18 with Mathematics categories.
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
Solving Nonlinear Equations With Newton S Method
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 2003-01-01
Solving Nonlinear Equations With Newton S Method written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
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.
Solving Nonlinear Equations With Newton S Method
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 2003-01-01
Solving Nonlinear Equations With Newton S Method written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Contains trouble-shooting guides to the major algorithms for Newton's method, their common failure modes, and the likely causes of failure.
New Developments Of Newton Type Iterations For Solving Nonlinear Problems
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Author : Tugal Zhanlav
language : en
Publisher: Springer Nature
Release Date :
New Developments Of Newton Type Iterations For Solving Nonlinear Problems written by Tugal Zhanlav and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Numerical Methods For Unconstrained Optimization And Nonlinear Equations
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Author : J. E. Dennis, Jr.
language : en
Publisher: SIAM
Release Date : 1996-12-01
Numerical Methods For Unconstrained Optimization And Nonlinear Equations written by J. E. Dennis, Jr. and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-01 with Mathematics categories.
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.
Introduction To Methods For Nonlinear Optimization
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Author : Luigi Grippo
language : en
Publisher: Springer Nature
Release Date : 2023-05-27
Introduction To Methods For Nonlinear Optimization written by Luigi Grippo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-27 with Mathematics categories.
This book has two main objectives: • to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level; • to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research. The basic material on unconstrained and constrained optimization is organized into two blocks of chapters: • basic theory and optimality conditions • unconstrained and constrained algorithms. These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors’ experience, is suitable for introductory courses. A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems. In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems. The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course.
The Numerical Solution Of Nonlinear Problems
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Author : Christopher T. H. Baker
language : en
Publisher: Oxford University Press, USA
Release Date : 1981
The Numerical Solution Of Nonlinear Problems written by Christopher T. H. Baker and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Language Arts & Disciplines categories.
Quasi Newton Methods For Nonlinear Programming
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Author : Jason Dean Hibbeler
language : en
Publisher:
Release Date : 1997
Quasi Newton Methods For Nonlinear Programming written by Jason Dean Hibbeler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Combinatorial optimization categories.
Abstract: "In this thesis, we examine nonlinear programming from the standpoint of nonlinear equations. We consider Newton and quasi-Newton algorithms for solving underdetermined nonlinear systems and then show how these techniques can be applied in the setting of constrained optimization. We produce new perturbation analyses for the special symmetric block system resulting from a standard solution method in nonlinear programming. Using the steepest descent method for unconstrained optimization, we develop a new iteration for the constrained case. We give a convergence analysis for this new method and illustrate its behavior with numerical examples. Finally, we propose a new class of symmetric updates for use in a quasi-Newton method for nonlinear programming. We show how these updates model the underlying nonlinear equation better than the standard symmetric updates and also how they require less overall work for large problems."
Semismooth Newton Methods For Variational Inequalities And Constrained Optimization Problems In Function Spaces
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Author : Michael Ulbrich
language : en
Publisher: SIAM
Release Date : 2011-01-01
Semismooth Newton Methods For Variational Inequalities And Constrained Optimization Problems In Function Spaces written by Michael Ulbrich and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Constrained optimization categories.
Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.