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Dynamical Systems Method for Solving Operator Equations

✍ Scribed by Alexander G. Ramm (Eds.)

Publisher
Elsevier Ltd
Year
2007
Tongue
English
Leaves
305
Series
Mathematics in Science and Engineering 208
Category
Library
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✦ Synopsis

The book 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)

✦ Table of Contents

Content:
Preface
Pages v-x

Chapter 1 Introduction
Pages 1-8

Chapter 2 Ill-posed problems
Pages 9-59

Chapter 3 DSM for well-posed problems
Pages 61-74

Chapter 4 DSM and linear ill-posed problems
Pages 75-95

Chapter 5 Some inequalities
Pages 97-108

Chapter 6 DSM for monotone operators
Pages 109-119

Chapter 7 DSM for general nonlinear operator equations
Pages 121-131

Chapter 8 DSM for operators satisfying a spectral assumption
Pages 133-139

Chapter 9 DSM in Banach spaces
Pages 141-148

Chapter 10 DSM and newton-type methods without inversion of the derivative
Pages 149-157

Chapter 11 DSM and unbounded operators
Pages 159-161

Chapter 12 DSM and nonsmooth operators
Pages 163-176

Chapter 13 DSM as a theoretical tool
Pages 177-182

Chapter 14 DSM and iterative methods
Pages 183-195

Chapter 15 Numerical problems arising in applications
Pages 197-239

Chapter 16 Auxiliary results from analysis
Pages 241-274

Bibliographical notes
Pages 275-277

Bibliography
Pages 279-287

Index
Pages 288-289

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