New Developments Of Newton Type Iterations For Solving Nonlinear Problems
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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.
New Developments Of Newton Type Iterations For Solving Nonlinear Problems
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Author : Tugal Zhanlav
language : en
Publisher: Springer
Release Date : 2024-08-19
New Developments Of Newton Type Iterations For Solving Nonlinear Problems written by Tugal Zhanlav and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-19 with Mathematics categories.
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.
Convergence And Applications Of Newton Type Iterations
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Author : Ioannis K. Argyros
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-12
Convergence And Applications Of Newton Type Iterations written by Ioannis K. Argyros 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 2008-06-12 with Mathematics categories.
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
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Author : Sergio Amat
language : en
Publisher: Springer
Release Date : 2016-09-27
Advances In Iterative Methods For Nonlinear Equations written by Sergio Amat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-27 with Mathematics categories.
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.
Iterative Methods For Linear And Nonlinear Equations
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 1995-01-01
Iterative Methods For Linear And Nonlinear Equations 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 1995-01-01 with Mathematics categories.
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.
Iterative Methods For Solving Nonlinear Equations And Systems
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Author : Juan R. Torregrosa
language : en
Publisher: MDPI
Release Date : 2019-12-06
Iterative Methods For Solving Nonlinear Equations And Systems written by Juan R. Torregrosa and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Mathematics categories.
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.
Newton Type Methods For Optimization And Variational Problems
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Author : Alexey F. Izmailov
language : en
Publisher: Springer
Release Date : 2014-07-08
Newton Type Methods For Optimization And Variational Problems written by Alexey F. Izmailov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Business & Economics categories.
This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.
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:
Release Date : 2003
Solving Nonlinear Equations With Newton S Method written by C. T. Kelley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Iterative methods (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.--[Source inconnue].
On Iterative Methods To Solve Nonlinear Equations
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Author : Maria Àngela Grau Gotés
language : en
Publisher:
Release Date : 2016
On Iterative Methods To Solve Nonlinear Equations written by Maria Àngela Grau Gotés and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Many of the problems in experimental sciences and other disciplines can be expressed in the form of nonlinear equations. The solution of these equations is rarely obtained in closed form. With the development of computers, these problems can be addressed by numerical algorithms that approximate the solution. Specifically, fixed point iterative methods are used, which generate a convergent sequence presumably to the solution of the equation or system of equations. Since J.F. Traub (Iterative methods for the solution of equations, Prentice-Hall, N.J. 1964) initiated the qualitative as well the quantitative analysis of iterative methods in the 1960s, iterative methods for nonlinear systems has been a constantly interesting field of study for numerical analysts. Our contribution to this field is the analysis and construction of new iterative methods, by improving the order of convergence and computational efficiency either of these or other known methods. To study the new iterative methods that we have proposed, we reviewed analyzed and improved classic concepts of computational order of convergence, the error equation, and the computational cost of an iterative method for both an equation and a system of nonlinear equations. Specifically, we have worked on the following points: - We computed the local order of convergence for known two-step and new multi-step iterative methods by means of expansions in formal developments in power series of the function F, the Jacobian operator, the inverse Jacobian operator and the divided difference operator and its inverse operator. - We generated some measures that approximate the order of convergence. Four new variants for computing the computational order of convergence (COC) are given: one requires the value of the root, whilst the other three do not. - We constructed families of iterative schemes that are variants of Newton's method and Chebyshev's method and improve the order and the efficiency. - We studied several families of the modified Secant method (Secant, Kurchatov and Steffensen), evaluated variants of these methods and chose the most efficient. - We generalized the concepts of efficiency index and computational efficiency for nonlinear equations to systems of nonlinear equations. This has been termed the computational efficiency index (CEI). - We considered that in iterative process using variable precision, the accuracy will increase as the computation proceeds. The final result will be obtained as precisely as possible, depending on the computer and the software. - We expressed the cost of evaluating elementary functions in terms of products. This cost depends on the computer, the software and the arithmetic that we used. The above numerical calculations were performed in the algebraic system called MAPLE. - We presented a new way of comparing elapsed time for different iterative schemes. This consists of estimating the time required to achieve a correct decimal of the solution by the method selected. That is, we measured the relationship between the time to fulfill the stop criterion and the total number of correct decimals obtained by method. The five papers selected for this compendium were published in scientific journals in the area of applied mathematics. The impact factor of these journals is, in all cases, in the first third according to the classification of the Journal of Citation Reports. There are four preceding papers that no are part of this report by its publication date.