Approximate Solutions Of Operator Equations
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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.
Approximate Solutions Of Operator Equations
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Author : Mingjun Chen
language : en
Publisher: World Scientific
Release Date : 1997-07-01
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 1997-07-01 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. Contents:IntroductionOperator Equations and Their Approximate Solutions (I): Compact Linear OperatorsOperator Equations and Their Approximate solutions (II): Other Linear OperatorsTopological Degrees and Fixed Point EquationsNonlinear Monotone Operator Equations and Their Approximate SolutionsOperator Evolution Equations and Their Projective Approximate Solutions Readership: Applied mathematicians, mathematical physicists, numerical analysts and electrical & mechanical engineers. keywords:Operator Evolution Equation;Nonlinear Operator Equation;Monotone Operator;Projective Approximation;Least-Squares Algorithm;Topological Degree;Fixed Point Theorem
Approximate Solution Of Operator Equations With Applications
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Author : Argyros Ioannis K
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-08-26
Approximate Solution Of Operator Equations With Applications written by Argyros Ioannis K and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-26 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 : 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.
Approximatesolution Of Operator Equations With Applications
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Author : Ioannis K. Argyros
language : en
Publisher:
Release Date : 2005
Approximatesolution Of Operator Equations With Applications written by Ioannis K. Argyros and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Linear Operator Equations
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Author : M. Thamban Nair
language : en
Publisher: World Scientific
Release Date : 2009
Linear Operator Equations 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 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.
Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space
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Author : W.M., III. Patterson
language : en
Publisher: Springer
Release Date : 2006-11-15
Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space written by W.M., III. Patterson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
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.
Optimization Of Methods For Approximate Solution Of Operator Equations
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Author : Sergei V. Pereverzev
language : en
Publisher: Nova Science Publishers
Release Date : 1996
Optimization Of Methods For Approximate Solution Of Operator Equations written by Sergei V. Pereverzev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Approximate Solution Of Random Equations
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Author : Albert T. Bharucha-Reid
language : en
Publisher: North-Holland
Release Date : 1979
Approximate Solution Of Random Equations written by Albert T. Bharucha-Reid and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Approximation theory categories.