Convergence and Applications of Newton-type Iterations

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

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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.

The Theory and Applications of Iteration Methods

The Theory and Applications of Iteration Methods
Title The Theory and Applications of Iteration Methods PDF eBook
Author Ioannis K. Argyros
Publisher CRC Press
Pages 356
Release 2022-01-21
Genre Mathematics
ISBN 1000536777

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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.

Iterative Methods and Their Dynamics with Applications

Iterative Methods and Their Dynamics with Applications
Title Iterative Methods and Their Dynamics with Applications PDF eBook
Author Ioannis Konstantinos Argyros
Publisher CRC Press
Pages 366
Release 2017-07-12
Genre Mathematics
ISBN 1498763626

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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.

Advances in Iterative Methods for Nonlinear Equations

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

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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.

Aspects of the Computational Theory for Certain Iterative Methods

Aspects of the Computational Theory for Certain Iterative Methods
Title Aspects of the Computational Theory for Certain Iterative Methods PDF eBook
Author Ioannis K. Argyros
Publisher Polimetrica s.a.s.
Pages 581
Release 2009
Genre Mathematics
ISBN 8876991514

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Advanced Mathematical Analysis and its Applications

Advanced Mathematical Analysis and its Applications
Title Advanced Mathematical Analysis and its Applications PDF eBook
Author Pradip Debnath
Publisher CRC Press
Pages 493
Release 2023-10-17
Genre Mathematics
ISBN 1000967263

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Advanced Mathematical Analysis and its Applications presents state-of-the-art developments in mathematical analysis through new and original contributions and surveys, with a particular emphasis on applications in engineering and mathematical sciences. New research directions are indicated in each of the chapters, and while this book is meant primarily for graduate students, there is content that will be equally useful and stimulating for faculty and researchers. The readers of this book will require minimum knowledge of real, complex, and functional analysis, and topology. Features Suitable as a reference for graduate students, researchers, and faculty Contains the most up-to-date developments at the time of writing.

Numerical Methods for Equations and its Applications

Numerical Methods for Equations and its Applications
Title Numerical Methods for Equations and its Applications PDF eBook
Author Ioannis K. Argyros
Publisher CRC Press
Pages 473
Release 2012-06-05
Genre Mathematics
ISBN 1466517115

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This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter co