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Iterative Methods For The Solutions Of Nonlinear Operator Equations In Hilbert Space
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Book Synopsis ITERATIVE METHODS FOR THE SOLUTIONS OF NONLINEAR OPERATOR EQUATIONS IN HILBERT SPACE. by : MOHAMMED ZUHAIR ZAKI NASHED
Download or read book ITERATIVE METHODS FOR THE SOLUTIONS OF NONLINEAR OPERATOR EQUATIONS IN HILBERT SPACE. written by MOHAMMED ZUHAIR ZAKI NASHED and published by . This book was released on 1963 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space by : W.M., III. Patterson
Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space written by W.M., III. Patterson and published by Springer. This book was released on 2006-11-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this expository work we shall conduct a survey of iterative techniques for solving the linear operator equations Ax=y in a Hilbert space. Whenever convenient these iterative schemes are given in the context of a complex Hilbert space -- Chapter II is devoted to those methods (three in all) which are given only for real Hilbert space. Thus chapter III covers those methods which are valid in a complex Hilbert space except for the two methods which are singled out for special attention in the last two chapters. Specifically, the method of successive approximations is covered in Chapter IV, and Chapter V consists of a discussion of gradient methods. While examining these techniques, our primary concern will be with the convergence of the sequence of approximate solutions. However, we shall often look at estimates of the error and the speed of convergence of a method.
Book Synopsis Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space - a Survey by : Walter Mead Patterson
Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space - a Survey written by Walter Mead Patterson and published by . This book was released on 1974 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for Nonlinear Operator Equations in Banach Spaces by : Shih-sen Chang
Download or read book Iterative Methods for Nonlinear Operator Equations in Banach Spaces written by Shih-sen Chang and published by Nova Science Publishers. This book was released on 2002 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Banach's fixed point theorem was proved by Banach in 1922, many authors have used this theorem to show the existence and uniqueness of solutions for differential and integral equations, a system of simultaneous linear algebraic equations by methods of successive approximations, etc., and have extended, generalised and improved this theorem in several ways. The purpose of this book is to give a comprehensive introduction to the study of iterative approximation methods for solutions of nonlinear equations involving some kinds of nonlinear mappings and multi-valued mappings in Banach spaces and normed linear spaces by the Mann and Ishikawa iterative sequences (with errors and mixed errors) and the generalised steepest descent approximations.
Book Synopsis Projection-iterative Methods for Solution of Operator Equations by : Nikolaĭ Stepanovich Kurpelʹ
Download or read book Projection-iterative Methods for Solution of Operator Equations written by Nikolaĭ Stepanovich Kurpelʹ and published by American Mathematical Soc.. This book was released on 1976 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods without Inversion by : Anatoly Galperin
Download or read book Iterative Methods without Inversion written by Anatoly Galperin and published by CRC Press. This book was released on 2016-11-17 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm’s and Broyden’s methods. Convergence analyses of the methods considered are based on Kantorovich’s majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity. Key Features The methods discussed are analyzed under the assumption of regular continuity of divided difference operator, which is more general and more flexible than the traditional Lipschitz continuity. An attention is given to criterions for comparison of merits of various methods and to the related concept of optimality of a method of certain class. Many publications on methods for solving nonlinear operator equations discuss methods that involve inversion of linearization of the operator, which task is highly problematic in infinite dimensions. Accessible for anyone with minimal exposure to nonlinear functional analysis.
Book Synopsis Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space by : W M III Patterson
Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space written by W M III Patterson and published by Springer. This book was released on 2014-01-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fixed Points of Nonlinear Operators by : Haiyun Zhou
Download or read book Fixed Points of Nonlinear Operators written by Haiyun Zhou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Methods for Fixed Points of Nonlinear Operators offers an introduction into iterative methods of fixed points for nonexpansive mappings, pseudo-contrations in Hilbert Spaces and in Banach Spaces. Iterative methods of zeros for accretive mappings in Banach Spaces and monotone mappings in Hilbert Spaces are also discussed. It is an essential work for mathematicians and graduate students in nonlinear analysis.
Book Synopsis Computational Solution of Nonlinear Operator Equations by : Louis B. Rall
Download or read book Computational Solution of Nonlinear Operator Equations written by Louis B. Rall and published by . This book was released on 1979 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamical Systems Method for Solving Nonlinear Operator Equations by : Alexander G. Ramm
Download or read book Dynamical Systems Method for Solving Nonlinear Operator Equations written by Alexander G. Ramm and published by Elsevier. This book was released on 2006-09-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author. Contains a systematic development of a novel general method, the dynamical systems method, DSM for solving operator equations, especially nonlinear and ill-posed Self-contained, suitable for wide audience Can be used for various courses for graduate students and partly for undergraduates (especially for RUE classes)
Book Synopsis Methods for Solution of Nonlinear Operator Equations by : Vitaliĭ Pavlovich Tanana
Download or read book Methods for Solution of Nonlinear Operator Equations written by Vitaliĭ Pavlovich Tanana and published by VSP. This book was released on 1997 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Book Synopsis Iterative Methods for the Solution of Linear Operator Equations in Hilbert Space by : Michael Luther Hines
Download or read book Iterative Methods for the Solution of Linear Operator Equations in Hilbert Space written by Michael Luther Hines and published by . This book was released on 1976 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for Ill-Posed Problems by : Anatoly B. Bakushinsky
Download or read book Iterative Methods for Ill-Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter. This book was released on 2010-12-23 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.
Book Synopsis Methods in Nonlinear Integral Equations by : R Precup
Download or read book Methods in Nonlinear Integral Equations written by R Precup and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.
Book Synopsis Iterative Methods for Solving Nonlinear Equations and Systems by : Juan R. Torregrosa
Download or read book Iterative Methods for Solving Nonlinear Equations and Systems written by Juan R. Torregrosa and published by MDPI. This book was released on 2019-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Polynomial Operator Equations in Abstract Spaces and Applications by : Ioannis K. Argyros
Download or read book Polynomial Operator Equations in Abstract Spaces and Applications written by Ioannis K. Argyros and published by CRC Press. This book was released on 2020-10-07 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques. Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings. Topics include: Special cases of nonlinear operator equations Solution of polynomial operator equations of positive integer degree n Results on global existence theorems not related with contractions Galois theory Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas Results on the various Chandrasekhar equations Weierstrass theorem Matrix representations Lagrange and Hermite interpolation Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space The materials discussed can be used for the following studies Advanced numerical analysis Numerical functional analysis Functional analysis Approximation theory Integral and differential equation
Book Synopsis Iterative Solution of Nonlinear Equations in Several Variables by : J. M. Ortega
Download or read book Iterative Solution of Nonlinear Equations in Several Variables written by J. M. Ortega and published by Elsevier. This book was released on 2014-05-10 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.
