Convergence and Applications of Newton-type Iterations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Convergence and Applications of Newton-type Iterations PDF full book. Access full book title Convergence and Applications of Newton-type Iterations by Ioannis K. Argyros. Download full books in PDF and EPUB format.
Author: Ioannis K. Argyros
Publisher: Springer Science & Business Media
ISBN: 0387727434
Category : Mathematics
Languages : en
Pages : 513
Get Book Here
Book Description
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.
Author: Ioannis K. Argyros
Publisher: Springer Science & Business Media
ISBN: 0387727434
Category : Mathematics
Languages : en
Pages : 513
Get Book Here
Book Description
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.
Author: Tugal Zhanlav
Publisher: Springer Nature
ISBN: 303163361X
Category :
Languages : en
Pages : 288
Get Book Here
Book Description
Author: Tugal Zhanlav
Publisher: Springer
ISBN: 9783031633607
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: Ioannis K. Argyros
Publisher: CRC Press
ISBN: 1000536750
Category : Mathematics
Languages : en
Pages : 471
Get Book Here
Book Description
The theory and applications of Iteration Methods is a very fast-developing field of numerical analysis and computer methods. The second edition is completely updated and continues to present the state-of-the-art contemporary theory of iteration methods with practical applications, exercises, case studies, and examples of where and how they can be used. The Theory and Applications of Iteration Methods, Second Edition includes newly developed iteration methods taking advantage of the most recent technology (computers, robots, machines). It extends the applicability of well-established methods by increasing the convergence domain and offers sharper error tolerance. New proofs and ideas for handling convergence are introduced along with a new variety of story problems picked from diverse disciplines. This new edition is for researchers, practitioners, and students in engineering, economics, and computational sciences.
Author: Juan R. Torregrosa
Publisher: MDPI
ISBN: 3039219405
Category : Mathematics
Languages : en
Pages : 494
Get Book Here
Book Description
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: C. T. Kelley
Publisher: SIAM
ISBN: 9780898718898
Category : Mathematics
Languages : en
Pages : 117
Get Book Here
Book Description
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: Ioannis Konstantinos Argyros
Publisher: CRC Press
ISBN: 1351649507
Category : Mathematics
Languages : en
Pages : 301
Get Book Here
Book Description
Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis. The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences or Applied Sciences. Moreover, the newest techniques used to study the dynamics of iterative methods are described and used in the book and they are compared with the classical ones.
Author: Sergio Amat
Publisher: Springer
ISBN: 9783319818450
Category : Mathematics
Languages : en
Pages : 286
Get Book Here
Book Description
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.
Author: K. Veselić
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
Get Book Here
Book Description
We give a new class of convergence criteria for the classical Newton method for the equation () = 0. We prove the global convergence, if the function is the gradient of a convex function, while the convergence in the general case is still open. Our convergence condition consists of only one bound with a constant, which is shown to be sharp. We apply our result to a generic variational problem as well to uniformly diagonally dominant Hessians. The convergence result is extended to the cases where the derivative is defined merely as a distribution.
Author: Wu Zhang
Publisher: Springer Science & Business Media
ISBN: 3642118410
Category : Computers
Languages : en
Pages : 602
Get Book Here
Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the Second International Conference on High Performance Computing and Applications, HPCA 2009, held in Shangahi, China, in August 2009. The 71 revised papers presented together with 10 invited presentations were carefully selected from 324 submissions. The papers cover topics such as numerical algorithms and solutions; high performance and grid computing; novel approaches to high performance computing; massive data storage and processsing; and hardware acceleration.
