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Iterative Methods for Ill-Posed Problems

An Introduction

Anatoly B. Bakushinsky, Mihail Yu. Kokurin, Alexandra Smirnova (Autoren)

Buch | Hardcover

XI, 136 Seiten

2010
De Gruyter (Verlag)
978-3-11-025064-0 (ISBN)

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The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

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.

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.

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

"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

Erscheint lt. Verlag	21.12.2010
Reihe/Serie	Inverse and Ill-Posed Problems Series ; 54
Zusatzinfo	10 b/w ill.
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	240 x 170 mm
Gewicht	399 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Hilbert-Räume • hilbert space • ill-posed problem • Ill-posed Problem; Inverse Problem; Iterative Method; Operator Equation; Hilbert Space • inverse problem • Iteration • Iterative Method • Operator Equation
ISBN-10	3-11-025064-0 / 3110250640
ISBN-13	978-3-11-025064-0 / 9783110250640
Zustand	Neuware