Iterative methods for ill-posed problems : an introduction
著者
書誌事項
Iterative methods for ill-posed problems : an introduction
（Inverse and ill-posed problems series, 54）
De Gruyter, c2010
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Итеративные методы решения некорректных задач
Iterativnye metody reshenii︠a︡ nekorrektnykh zadach
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注記
Includes bibliographical references (p. [132]-136) and index
内容説明・目次
内容説明
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.
目次
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
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