Newton S Method An Updated Approach Of Kantorovich S Theory
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Newton S Method
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Author : José Antonio Ezquerro Fernández
language : en
Publisher:
Release Date : 2017
Newton S Method written by José Antonio Ezquerro Fernández and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Computer science categories.
Newton S Method An Updated Approach Of Kantorovich S Theory
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Author : José Antonio Ezquerro Fernández
language : en
Publisher: Birkhäuser
Release Date : 2017-07-05
Newton S Method An Updated Approach Of Kantorovich S Theory written by José Antonio Ezquerro Fernández and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-05 with Mathematics categories.
This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.
Mild Differentiability Conditions For Newton S Method In Banach Spaces
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Author : José Antonio Ezquerro Fernandez
language : en
Publisher: Springer Nature
Release Date : 2020-07-03
Mild Differentiability Conditions For Newton S Method In Banach Spaces written by José Antonio Ezquerro Fernandez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-03 with Mathematics categories.
In this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors’ technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich’s majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type and, second, it improves the results obtained through majorizing sequences. In addition, the authors extend the application of Newton’s method in Banach spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich’s theory for Newton’s method is substantially broadened. Moreover, this technique can be applied to any iterative method. This book is chiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis.
The Merging Of Disciplines New Directions In Pure Applied And Computational Mathematics
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Author : Richard E. Ewing
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Merging Of Disciplines New Directions In Pure Applied And Computational Mathematics written by Richard E. Ewing 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 2012-12-06 with Mathematics categories.
This volume is the Proceedings of the symposium held at the University of Wyoming in August, 1985, to honor Gail Young on his seventieth birthday (which actually took place on October 3, 1985) and on the occasion of his retirement. Nothing can seem more natural to a mathematician in this country than to honor Gail Young. Gail embodies all the qualities that a mathematician should possess. He is an active and effective research mathematician, having written over sixty pa pers in topology, n-dimensional analysis, complex variables, and "miscellanea." He is an outstanding expositor, as his fine book Topology, written with J. G. Hocking (Addison Wesley, 1961), amply demonstrates. He has a superlative record in public office of outstanding, unstinting service to the mathematical community and to the cause of education. But what makes Gail unique and special is that throughout all aspects of his distinguished career, he has emphasized human values in everything he has done. In touching the lives of so many of us, he has advanced the entire profession. Deservedly, he has innumerable friends in the mathematical community, the academic community, and beyond.
Computational Theory Of Iterative Methods
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Author : Ioannis Argyros
language : en
Publisher: Elsevier
Release Date : 2007-09-04
Computational Theory Of Iterative Methods written by Ioannis Argyros and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-04 with Mathematics categories.
The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory. - Latest convergence results for the iterative methods - Iterative methods with the least computational cost - Iterative methods with the weakest convergence conditions - Open problems on iterative methods
From Topology To Computation Proceedings Of The Smalefest
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Author : Morris W. Hirsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
From Topology To Computation Proceedings Of The Smalefest written by Morris W. Hirsch 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 2012-12-06 with Mathematics categories.
An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati cians working in the many fields to which Smale has made lasting con tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.
Computational Methods In Nonlinear Analysis Efficient Algorithms Fixed Point Theory And Applications
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Author : Ioannis K Argyros
language : en
Publisher: World Scientific
Release Date : 2013-07-11
Computational Methods In Nonlinear Analysis Efficient Algorithms Fixed Point Theory And Applications written by Ioannis K Argyros and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-11 with Mathematics categories.
The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory.This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.
Efficient Methods For Solving Equations And Variational Inequalities
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Author : Ioannis K. Argyros
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2009
Efficient Methods For Solving Equations And Variational Inequalities written by Ioannis K. Argyros and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Iterative Methods And Their Dynamics With Applications
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Author : Ioannis Konstantinos Argyros
language : en
Publisher: CRC Press
Release Date : 2017-07-12
Iterative Methods And Their Dynamics With Applications written by Ioannis Konstantinos Argyros and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Mathematics categories.
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.
The Theory And Applications Of Iteration Methods
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Author : Ioannis K. Argyros
language : en
Publisher: CRC Press
Release Date : 2022-01-21
The Theory And Applications Of Iteration Methods written by Ioannis K. Argyros and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-21 with Mathematics categories.
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.
