Dynamical Systems Method for Solving Nonlinear Operator Equations

By

  • Alexander Ramm, Kansas State University, Manhattan, KS, USA

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 provedin the book, and some of the background material is also included. The results presented are mostly obtained by the author.
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Audience

Mathematicians, numerical analysists, specialists in scientific computing, engineers and others interested in solving operator equations, ill-posed and inverse problems.

 

Book information

  • Published: September 2006
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-52795-0


Table of Contents

PrefaceContents 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 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 analysisBibliographical notesBibliographyIndex