Methods For Solving Operator Equations

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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.

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.

Dynamical Systems Method For Solving Nonlinear Operator Equations

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Author : Alexander G. Ramm
language : en
Publisher: Elsevier
Release Date : 2006-09-25

Dynamical Systems Method For Solving Nonlinear Operator Equations written by Alexander G. Ramm and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-25 with Mathematics categories.

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)

Methods For Solving Operator Equations

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Author : Vitaliĭ Pavlovich Tanana
language : en
Publisher:
Release Date :

Methods For Solving Operator Equations written by Vitaliĭ Pavlovich Tanana and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with 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.

Non Iterative Methods For Solving Operator Equations Of The First Kind

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Author : John W. Hilgers
language : en
Publisher:
Release Date : 1973

Non Iterative Methods For Solving Operator Equations Of The First Kind written by John W. Hilgers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Operator equations categories.

The paper compares the reproducing kernel Hilbert space method for solving integral equations of the first kind with Tihonov regularization. The methods are theoretically identical and differ in practice only in the way discretization is introduced. Numerical examples are given. (Author).

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.

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.

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 : Walter Mead Patterson
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1974-07-22

Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space written by Walter Mead Patterson and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-07-22 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.