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Description
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.
Key Features
- 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)
Readership
Mathematicians, numerical analysists, specialists in scientific computing, engineers and others interested in solving operator equations, ill-posed and inverse problems.
Table of Contents
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
Details
- No. of pages:
- 304
- Language:
- English
- Copyright:
- © 2007
- Published:
- 25th September 2006
- Imprint:
- Elsevier Science
- eBook ISBN:
- 9780080465562
- Print ISBN:
- 9780444527950
- Print ISBN:
- 9780444550811
About the author
Alexander Ramm
Affiliations and Expertise
Kansas State University, Manhattan, KS, USA