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Dynamical Systems Method for Solving Nonlinear Operator Equations, Vol 208. Mathematics in Science and Engineering - Product Image

Dynamical Systems Method for Solving Nonlinear Operator Equations, Vol 208. Mathematics in Science and Engineering

  • ID: 1759887
  • September 2006
  • 304 Pages
  • Elsevier Science and Technology

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)

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

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