Iterative Methods for Ill-Posed Problems
An Introduction
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ISBN-13:
9783110250640
Veröffentl:
2010
Einband:
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Erscheinungsdatum:
21.12.2010
Seiten:
152
Autor:
Anatoly B. Bakushinsky
Gewicht:
448 g
Format:
246x175x14 mm
Serie:
54, ISSN
Sprache:
Englisch
Beschreibung:
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.
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1 Regularity Condition. Newton's Method2 The Gauss-Newton Method3 The Gradient Method4 Tikhonov's Scheme5 Tikhonov's Scheme for Linear Equations6 The Gradient Scheme for Linear Equations7 Convergence Rates for the Approximation Methods in the Case of Linear Irregular Equations8 Equations with a Convex Discrepancy Functional by Tikhonov's Method9 Iterative Regularization Principle10 The Iteratively Regularized Gauss-Newton Method11 The Stable Gradient Method for Irregular Nonlinear Equations12 Relative Computational Efficiency of Iteratively Regularized Methods13 Numerical Investigation of Two-Dimensional Inverse Gravimetry Problem14 Iteratively Regularized Methods for Inverse Problem in Optical Tomography15 Feigenbaum's Universality Equation16 ConclusionReferencesIndex¿
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