Approximate Solutions Of Operator Equations
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Approximate Solutions Of Operator Equations
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Author : Mingjun Chen
language : en
Publisher: World Scientific
Release Date : 1997
Approximate Solutions Of Operator Equations written by Mingjun Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates. The operator equations under investigation include various linear and nonlinear types of ordinary and partial differential equations, integral equations, and abstract evolution equations, which are frequently involved in applied mathematics and engineering applications.Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations.
Approximate Solution Of Operator Equations
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Author : Mark Aleksandrovich Krasnoselʹskiĭ
language : en
Publisher:
Release Date : 1969
Approximate Solution Of Operator Equations written by Mark Aleksandrovich Krasnoselʹskiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Approximate Solution Of Operator Equations With Applications
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Author : Ioannis K. Argyros
language : en
Publisher: World Scientific
Release Date : 2005
Approximate Solution Of Operator Equations With 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 2005 with Mathematics categories.
Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.
Approximate Solution Of Operator Equations
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Author : M.A. Krasnosel'skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approximate Solution Of Operator Equations written by M.A. Krasnosel'skii 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.
One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.
Linear Operator Equations Approximation And Regularization
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Author : M Thamban Nair
language : en
Publisher: World Scientific
Release Date : 2009-05-05
Linear Operator Equations Approximation And Regularization written by M Thamban Nair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-05 with Mathematics categories.
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Projection Iterative Methods For Solution Of Operator Equations
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Author : Nikolaĭ Stepanovich Kurpelʹ
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
Projection Iterative Methods For Solution Of Operator Equations written by Nikolaĭ Stepanovich Kurpelʹ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Generalized Solutions Of Operator Equations And Extreme Elements
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Author : D.A. Klyushin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Generalized Solutions Of Operator Equations And Extreme Elements written by D.A. Klyushin 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 2011-10-05 with Mathematics categories.
Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.
Iterative Methods For Approximate Solution Of Inverse Problems
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Author : A.B. Bakushinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-28
Iterative Methods For Approximate Solution Of Inverse Problems written by A.B. Bakushinsky 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 2007-09-28 with Mathematics categories.
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.
Random Integral Equations
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Author : Bharucha-Reid
language : en
Publisher: Academic Press
Release Date : 1973-03-02
Random Integral Equations written by Bharucha-Reid and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-03-02 with Computers categories.
Random Integral Equations
Methods For Solving Operator Equations
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Author : V. P. Tanana
language : en
Publisher: Walter de Gruyter
Release Date : 2012-02-13
Methods For Solving Operator Equations written by V. P. Tanana and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-13 with Mathematics categories.
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.