Bakushinsky / Kokurin / Smirnova Iterative Methods for Ill-Posed Problems

An Introduction
1. Auflage 2010
ISBN: 978-3-11-025065-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 54, 147 Seiten

Reihe: Inverse and Ill-Posed Problems Series

Autoren/Hrsg.

Bakushinsky, Anatoly B.

Kokurin, Mihail Yu.

Smirnova, Alexandra

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)

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

Bakushinsky, Anatoly B.
Anatoly Bakushinsky, Institute of System Analysis of Institute of Russian Academy of Sciences (ISA RAS), Moscow, Russia;

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