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)


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


No. of pages:
© 2007
Elsevier Science
eBook ISBN:
Print ISBN:
Print ISBN:

About the author

Alexander Ramm

Affiliations and Expertise

Kansas State University, Manhattan, KS, USA