Theory of Tikhonov Regularization for Fredholm Equations of the First Kind

Cover

The theory of Tikhonov regularization for Fredholm equations of the first kind

© C W Groetsch 1984

     ISBN 0273086421

Preface

Contents

1 Introduction and preliminaries

     1.1. Equations of the first kind; ill-posed problems

     1.2. Linear ape rators in Hilbert space

     1.3. Generalized inverses

     REFERENCES

2 A general regularization method

     2.1. Convergence results

     2.2. Convergence rates

     2.3. Regularization with inexact data

     2.4. Some examples

     REFERENCES

3 Tikhonov regularization

     3.1. Tikhotiov\'s method

     3.2. Saturation and converse results

     3.3. The discrepancy principle

     3.4. Lise of differential operators

     REFERENCES

4 Finite dimensional approximations

     4.1. Finite rank approxinations

     4.2. A re uiarized Ritz a proach

     4.3. Marti`s method

     4.4. Monent discretization and cross validation.

     REFERENCES

List of symbols

Subject index