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Dynamical Systems Method for Solving Nonlinear Operator Equations
ID: 171881
Alexander Ramm
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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 usually obtained by the author.
- Contains a systematic development of a novel general method, the DSM for solving operator equations, especially nonlinear and ill-posed
- Self-contained, suitable for wide audience
- Can not be used for graduate students and partly for undergraduates (especially for RUE classes)
Preface
Contents
1. Introduction
2. Ill-posed problems
3. DSM for well-posed problems
4. DSM and linear ill-posed problems
5. Some inequalities
6. DSM for monotone operators
7. DSM for general nonlinear operator equations
8 DSM for operators satisfying a spectral assumption
9. DSM in Banach spaces
10. DSM and Newton-type methods without inversion of the derivative
11. DSM and unbounded operators
12. DSM and nonsmooth operators
13. DSM as a theoretical tool
14. DSM and iterative methods
15. Numerical problems arising in applications
16. Auxiliary results from analysis
Bibliographical notes
Bibliography
index
in the book, and some of the background material is also included. The results presented are usually obtained by the author.
- Contains a systematic development of a novel general method, the DSM for solving operator equations, especially nonlinear and ill-posed
- Self-contained, suitable for wide audience
- Can not be used for graduate students and partly for undergraduates (especially for RUE classes)
Preface
Contents
1. Introduction
2. Ill-posed problems
3. DSM for well-posed problems
4. DSM and linear ill-posed problems
5. Some inequalities
6. DSM for monotone operators
7. DSM for general nonlinear operator equations
8 DSM for operators satisfying a spectral assumption
9. DSM in Banach spaces
10. DSM and Newton-type methods without inversion of the derivative
11. DSM and unbounded operators
12. DSM and nonsmooth operators
13. DSM as a theoretical tool
14. DSM and iterative methods
15. Numerical problems arising in applications
16. Auxiliary results from analysis
Bibliographical notes
Bibliography
index
171881
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Alexander Ramm