Iterative Methods for Ill-Posed Problems

An Introduction
1. Auflage 2010
ISBN: 978-3-11-025064-0
Verlag: De Gruyter

Buch, Englisch, 136 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 448 g

Reihe: ISSN

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.

Zielgruppe

Mathematical Physicists, Theoretical Physicists, Mathematicians; / Mathematical physicists, theoretical physicists, mathematicians;

Autoren/Hrsg.

Bakushinsky, Anatoly B.

Smirnova, Alexandra

Kokurin, Mihail Yu.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

Frontmatter
Preface
Contents
1 The 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

Über Autor(innen)

Kokurin, Mihail Yu.
Mihail Kokurin, Mari State University, Russia;

Smirnova, Alexandra
Alexandra Smirnova, Georgia State University, Atlanta, Georgia, USA.

Bakushinsky, Anatoly B.
Anatoly Bakushinsky, Institute of System Analysis RAS, Moscow, Russia;

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.