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Methods for Solving Operator Equations

2012-02-13 Mathematics
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Release : 2012-02-13
Genre : Mathematics
Kind : eBook
Book Rating : 157/5 ( reviews)

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Book Synopsis Methods for Solving Operator Equations by : V. P. Tanana

Download or read book Methods for Solving Operator Equations written by V. P. Tanana. This book was released on 2012-02-13. 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.

Approximate Solution of Operator Equations

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 153/5 ( reviews)

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Book Synopsis Approximate Solution of Operator Equations by : M.A. Krasnosel'skii

Download or read book Approximate Solution of Operator Equations written by M.A. Krasnosel'skii. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

2006-09-25 Mathematics
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Release : 2006-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 560/5 ( reviews)

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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. This book was released on 2006-09-25. 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)

Methods for Solving Operator Equations

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Book Synopsis Methods for Solving Operator Equations by : Vitaliĭ Pavlovich Tanana

Download or read book Methods for Solving Operator Equations written by Vitaliĭ Pavlovich Tanana. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
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Book Rating : 553/5 ( reviews)

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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. This book was released on 2006-11-15. 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.

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