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)
Author(s): Alexander G. Ramm (Eds.)
Series: Mathematics in Science and Engineering 208
Publisher: Elsevier Ltd
Year: 2007
Language: English
Pages: 1-289
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
