Iterative Methods for Ill-Posed Problems : : An Introduction / / Anatoly B. Bakushinsky, Alexandra Smirnova, Mihail Yu. Kokurin.
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 assoc...
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Superior document: | Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 |
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VerfasserIn: | |
Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2010] ©2011 |
Year of Publication: | 2010 |
Language: | English |
Series: | Inverse and Ill-Posed Problems Series ,
54 |
Online Access: | |
Physical Description: | 1 online resource (136 p.) |
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Other title: | 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 |
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Summary: | 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. |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110250657 9783110238570 9783110238471 9783110637205 9783110233544 9783110233551 9783110233636 |
ISSN: | 1381-4524 ; |
DOI: | 10.1515/9783110250657 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Anatoly B. Bakushinsky, Alexandra Smirnova, Mihail Yu. Kokurin. |