Iterative Methods for Ill-Posed Problems - An Introduction

Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions.
Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

List of contents

1 Regularity Condition. Newton's Method
2 The Gauss-Newton Method
3 The Gradient Method
4 Tikhonov's Scheme
5 Tikhonov's Scheme for Linear Equations
6 The Gradient Scheme for Linear Equations
7 Convergence Rates for the Approximation Methods in the Case of Linear Irregular Equations
8 Equations with a Convex Discrepancy Functional by Tikhonov's Method
9 Iterative Regularization Principle
10 The Iteratively Regularized Gauss-Newton Method
11 The Stable Gradient Method for Irregular Nonlinear Equations
12 Relative Computational Efficiency of Iteratively Regularized Methods
13 Numerical Investigation of Two-Dimensional Inverse Gravimetry Problem
14 Iteratively Regularized Methods for Inverse Problem in Optical Tomography
15 Feigenbaum's Universality Equation
16 Conclusion
References
Index

About the author

Anatoly B. Bakushinsky, Institute of System Analysis,Russian Academy of Sciences, Moscow, Russia; Mihail Yu. Kokurin, Mari State Technical University, Yoshkar-Ola, Russia; Alexandra Smirnova, Georgia State University, Atlanta, Georgia, USA.

Report

"The book is an introduction to iterative methods for ill-posed problems. The style of writing is very user-friendly, in the best tradition of the Russian mathematical school. It is a valuable addition to the literature of ill-posed problems."
Anton Suhadolc in: University of Michigan Mathematical Reviews 2012c

Product details

• Authors: Anatoly Bakushinsky, Anatoly B Bakushinsky, Anatoly B. Bakushinsky, Mihail Y Kokurin, Mihail Y. Kokurin, Mihail Yu Kokurin, Mihail Yu. Kokurin, Smirnova, Alexandra Smirnova
• Publisher: De Gruyter
• Languages: English
• Product format: Hardback
• Released: 24.01.2011
• EAN: 9783110250640
• ISBN: 978-3-11-025064-0
• No. of pages: 136
• Dimensions: 174 mm x 170 mm x 244 mm
• Weight: 399 g
• Illustrations: 10 b/w ill.
• Series: Inverse and Ill-Posed Problems Series; Inverse and III-Posed Problems Series; Inverse and Ill-Posed Problems Series; Inverse and III-Posed Problems Series; ISSN
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > General, dictionaries; Mathematik, Analysis, Enzyklopädie, Infinitesimalrechnung, Calculus, Mathematische Physik, MATHEMATICS / General, Physik / Mathematik, Mathematische Analysis, allgemein, MATHEMATICS / Functional Analysis, MATHEMATICS / Mathematical Analysis