Computational Methods in Nonlinear Analysis

Download or read book Computational Methods in Nonlinear Analysis 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. Contents:Newton's MethodsSpecial Conditions for Newton's MethodNewton's Method on Special SpacesSecant MethodGauss–Newton MethodHalley's MethodChebyshev's MethodBroyden's MethodNewton-like MethodsNewton–Tikhonov Method for Ill-posed Problems Readership: Graduate students and researchers in computational mathematics and nonlinear analysis. Keywords:Numerical Analysis;Nonlinear Equations;Nonlinear Analysis;Variational Inequalities;Fixed Point TheoryKey Features:The book contains recent results in the field of computational sciencesThe book updates the results of the 3 competing books: (1) Convergence and Applications of Newton-type iterations, springer–Verlag Publ., 2008 (author: Ioannis K Argyros) (2) Functional Analysis, Pergamon Press, Oxford, 1982 (authors: L V Kantorovich, G P Akilov) (3) Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970 (authors: L M Ortega, W C Rheinboldt)The book presents several applications and examples in engineering, mathematical physics, optimization and many other areasReviews: “This book is known as a reference book for advanced computational methods in nonlinear analysis.” Zentralblatt MATH “The material included in the monograph is new and mainly due to its authors. It synthesises the deep and long-standing research activity in the field. This book is mainly intended for researchers working in the area of theoretical computational methods but it could also be an important documentation source for practitioners in applied computational mathematics.” Mathematical Reviews Clippings