Iterative methods for approximate solution of inverse problems /
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| Author / Creator: | Bakushinskiĭ, A. B. (Anatoliĭ Borisovich) |
|---|---|
| Imprint: | Dordrecht ; [Great Britain] : Springer, c2004. |
| Description: | xv, 291 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Mathematics and its applications ; v. 577 Mathematics and its applications (D. Reidel Publishing Company) ; v. 577 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5647042 |
Table of Contents:
- Dedication
- Acknowledgments
- Introduction
- 1. Irregular Equations As Ill-Posed Problems
- 1.1. Preliminaries
- 1.2. Irregular Equations and Contemporary Theory of Ill-Posed Problems
- 2. Regularization Methods for Linear Equations
- 2.1. General Scheme of Constructing Affine Regularization Algorithms for Linear Equations in Hilbert Space
- 2.2. General Scheme of Constructing Regularization Algorithms in Banach Space
- 2.3. Necessity of Sourcewise Representation for Rate of Convergence Estimates in Banach Space
- 3. Parametric Approximations of Solutions to Nonlinear Operator Equations
- 3.1. Classical Linearization Schemes
- 3.2. Parametric Approximations of Irregular Equations
- 3.3. Parametric Approximations in Inverse Scattering Problem
- 4. Iterative Processes on the Basis of Parametric Approximations
- 4.1. Generalized Gauss-Newton Type Methods for Nonlinear Irregular Equations in Hilbert Space
- 4.2. Necessity of Sourcewise Representation for Rate of Convergence Estimates of Gauss-Newton Type Methods
- 4.3. Generalized Newton-Kantorovich Type Methods for Nonlinear Irregular Equations in Banach Space
- 4.4. Necessity of Sourcewise Representation for Rate of Convergence Estimates of Newton-Kantorovich Type Methods
- 4.5. Continuous Methods for Irregular Operator Equations in Hilbert and Banach Spaces
- 5. Stable Iterative Processes
- 5.1. Stable Gradient Projection Methods with Adaptive Choice of Projectors
- 5.2. Projection Method with a Priori Choice of Projectors
- 5.3. Projection Method for Finding Quasisolutions
- 5.4. Stable Methods on the Basis of Parametric Approximations
- 5.5. Stable Continuous Approximations and Attractors of Dynamical Systems in Hilbert Space
- 5.6. Iteratively Regularized Gradient Method and Its Continuous Version
- 5.7. On Construction of Stable Iterative Methods for Smooth Irregular Equations and Equations with Discontinuous Operators
- 6. Applications of Iterative Methods
- 6.1. Reconstruction of Bounded Homogeneous Inclusion
- 6.2. Reconstruction of Separating Surface of Homogeneous Media by Measurements of Gravitational Attraction Force
- 6.3. Acoustic Inverse Medium Problem
- 6.4. Inverse Acoustic Obstacle Scattering. Far Field Observation
- 6.5. Inverse Acoustic Obstacle Scattering. Near Field Observation
- 7. Notes
- References
- Index
