New Developments of Newton-Type Iterations for Solving Nonlinear Problems
Title | New Developments of Newton-Type Iterations for Solving Nonlinear Problems PDF eBook |
Author | Tugal Zhanlav |
Publisher | Springer Nature |
Pages | 288 |
Release | |
Genre | |
ISBN | 303163361X |
New Developments of Newton-Type Iterations for Solving Nonlinear Problems
Title | New Developments of Newton-Type Iterations for Solving Nonlinear Problems PDF eBook |
Author | Tugal Zhanlav |
Publisher | Springer |
Pages | 0 |
Release | 2024-08-19 |
Genre | Mathematics |
ISBN | 9783031633607 |
This comprehensive book delves into the intricacies of Newton-type methods for nonlinear equations, offering insights into their convergence, accelerations, and extensions. Divided into three parts, the book explores higher-order iterations for systems of nonlinear equations and their applications in linear algebra. Emphasizing the pivotal role of iteration parameters in shaping convergence and expanding the domain, the authors draw from their extensive collaborative research to systematically compile and elucidate these findings. Catering to readers, graduate students, and researchers in applied mathematics, numerical analysis, and related disciplines, this book serves as a valuable resource, synthesizing decades of research to advance understanding and practical application in the field.
New Developments of Newton-type Iterations for Solving Nonlinear Problems
Title | New Developments of Newton-type Iterations for Solving Nonlinear Problems PDF eBook |
Author | Tugalyn Zhanlav |
Publisher | |
Pages | 0 |
Release | 2022 |
Genre | Calculus of variations |
ISBN | 9785907535480 |
Convergence and Applications of Newton-type Iterations
Title | Convergence and Applications of Newton-type Iterations PDF eBook |
Author | Ioannis K. Argyros |
Publisher | Springer Science & Business Media |
Pages | 513 |
Release | 2008-06-12 |
Genre | Mathematics |
ISBN | 0387727434 |
This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for an advanced course on numerical functional analysis.
Advances in Iterative Methods for Nonlinear Equations
Title | Advances in Iterative Methods for Nonlinear Equations PDF eBook |
Author | Sergio Amat |
Publisher | Springer |
Pages | 286 |
Release | 2016-09-27 |
Genre | Mathematics |
ISBN | 331939228X |
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.
Solving Nonlinear Equations with Newton's Method
Title | Solving Nonlinear Equations with Newton's Method PDF eBook |
Author | C. T. Kelley |
Publisher | SIAM |
Pages | 117 |
Release | 2003-01-01 |
Genre | Mathematics |
ISBN | 9780898718898 |
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.
Iterative Methods for Linear and Nonlinear Equations
Title | Iterative Methods for Linear and Nonlinear Equations PDF eBook |
Author | C. T. Kelley |
Publisher | SIAM |
Pages | 179 |
Release | 1995-01-01 |
Genre | Mathematics |
ISBN | 9781611970944 |
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.