Iterative Methods for Ill-Posed Problems
An Introduction
(Sprache: Englisch)
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...
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Klappentext zu „Iterative Methods for Ill-Posed Problems “
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.
Inhaltsverzeichnis zu „Iterative Methods for Ill-Posed Problems “
1 Regularity Condition. Newton's Method2 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
Autoren-Porträt von Anatoly B. Bakushinsky, Mihail Y. Kokurin, Alexandra Smirnova
Anatoly Bakushinsky, Institute of System Analysis RAS, Moscow, Russia; Mihail Kokurin, Mari State University, Russia; Alexandra Smirnova, Georgia State University, Atlanta, Georgia, USA.
Bibliographische Angaben
- Autoren: Anatoly B. Bakushinsky , Mihail Y. Kokurin , Alexandra Smirnova
- 2010, XI, 136 Seiten, 10 Schwarz-Weiß-Abbildungen, mit Abbildungen, Maße: 17,5 x 24,6 cm, Gebunden, Englisch
- Verlag: De Gruyter
- ISBN-10: 3110250640
- ISBN-13: 9783110250640
- Erscheinungsdatum: 24.01.2011
Sprache:
Englisch
Pressezitat
"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
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