Newton Methods For Nonlinear Problems PDF Download
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Author | : Peter Deuflhard |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2005-01-13 |
Genre | : Mathematics |
ISBN | : 9783540210993 |
Download Newton Methods for Nonlinear Problems Book in PDF, ePub and Kindle
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.
Author | : C. T. Kelley |
Publisher | : SIAM |
Total Pages | : 117 |
Release | : 2003-01-01 |
Genre | : Mathematics |
ISBN | : 9780898718898 |
Download Solving Nonlinear Equations with Newton's Method Book in PDF, ePub and Kindle
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 | : Peter Deuflhard |
Publisher | : Springer Science & Business Media |
Total Pages | : 432 |
Release | : 2011-09-18 |
Genre | : Mathematics |
ISBN | : 3642238998 |
Download Newton Methods for Nonlinear Problems Book in PDF, ePub and Kindle
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.
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 | : C. T. Kelley |
Publisher | : SIAM |
Total Pages | : 179 |
Release | : 1995-01-01 |
Genre | : Mathematics |
ISBN | : 9781611970944 |
Download Iterative Methods for Linear and Nonlinear Equations Book in PDF, ePub and Kindle
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 | : Peter Deuflhard |
Publisher | : Springer |
Total Pages | : 500 |
Release | : 2016-09-11 |
Genre | : Mathematics |
ISBN | : 9783642114656 |
Download Newton Methods for Nonlinear Problems Book in PDF, ePub and Kindle
Author | : Michael Ulbrich |
Publisher | : SIAM |
Total Pages | : 315 |
Release | : 2011-07-28 |
Genre | : Mathematics |
ISBN | : 1611970687 |
Download Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces Book in PDF, ePub and Kindle
A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.
Author | : Hans Petter Langtangen |
Publisher | : Springer |
Total Pages | : 522 |
Release | : 2017-06-21 |
Genre | : Computers |
ISBN | : 3319554565 |
Download Finite Difference Computing with PDEs Book in PDF, ePub and Kindle
This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
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.
Author | : Tugal Zhanlav |
Publisher | : Springer Nature |
Total Pages | : 288 |
Release | : |
Genre | : |
ISBN | : 303163361X |
Download New Developments of Newton-Type Iterations for Solving Nonlinear Problems Book in PDF, ePub and Kindle