Download or read book Newton s Method an Updated Approach of Kantorovich s Theory written by José Antonio Ezquerro Fernández and published by Birkhäuser. This book was released on 2017-07-05 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mild Differentiability Conditions for Newton s Method in Banach Spaces written by José Antonio Ezquerro Fernandez and published by Springer Nature. This book was released on 2020-07-03 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Merging of Disciplines New Directions in Pure Applied and Computational Mathematics written by Richard E. Ewing and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Computational Theory of Iterative Methods written by Ioannis Argyros and published by Elsevier. This book was released on 2007-09-04 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book From Topology to Computation Proceedings of the Smalefest written by Morris W. Hirsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Computational Methods In Nonlinear Analysis Efficient Algorithms Fixed Point Theory And Applications written by Ioannis K Argyros and published by World Scientific. This book was released on 2013-07-11 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advances in Iterative Methods for Nonlinear Equations written by Sergio Amat and published by Springer. This book was released on 2016-09-27 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Iterative Methods and Their Dynamics with Applications written by Ioannis Konstantinos Argyros and published by CRC Press. This book was released on 2017-07-12 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Efficient Methods for Solving Equations and Variational Inequalities written by Ioannis K. Argyros and published by Polimetrica s.a.s.. This book was released on 2009 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maple in Mathematics Education and Research written by Robert M. Corless and published by Springer Nature. This book was released on 2021-07-19 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes refereed proceedings of the 4th Maple Conference, MC 2020, held in Waterloo, Ontario, Canada, in November 2020. The 25 revised full papers and 3 short papers were carefully reviewed and selected out of 75 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.

Download or read book The Theory and Applications of Iteration Methods written by Ioannis K. Argyros and published by CRC Press. This book was released on 2022-01-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Collected Papers Of Stephen Smale The In 3 Volumes Volume 3 written by Roderick S C Wong and published by World Scientific. This book was released on 2000-06-30 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

Download or read book Aspects of the Computational Theory for Certain Iterative Methods written by Ioannis K. Argyros and published by Polimetrica s.a.s.. This book was released on 2009 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Unconstrained Optimization and Quantum Calculus written by Bhagwat Ram and published by Springer Nature. This book was released on with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Integral and Integro Differential Equations written by Harendra Singh and published by Springer Nature. This book was released on 2021-04-16 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations

Download or read book Computing And Analysing Energy Minimisation Problems In Liquid Crystals Implementation Using Firedrake written by Jingmin Xia and published by World Scientific. This book was released on 2023-05-22 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects?There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc.This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems.

Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.