Dynamical Systems Method for Solving Nonlinear Operator Equations: Volume 208

ISBN-13: 9780444527950 / Angielski / Twarda / 2006 / 289 str.

Alexander G. Ramm

Opis

Dynamical Systems Method for Solving Nonlinear Operator Equations 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)

Spis treści

1. Introduction2. Ill-posed problems3. DSM for well-posed problems4. DSM and linear ill-posed problems5. Some inequalities6. DSM for monotone operators7. DSM for general nonlinear operator equations8 DSM for operators satisfying a spectral assumption9. DSM in Banach spaces10. DSM and Newton-type methods without inversion of the derivative11. DSM and unbounded operators12. DSM and nonsmooth operators13. DSM as a theoretical tool14. DSM and iterative methods15. Numerical problems arising in applications16. Auxiliary results from analysis