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Ill-posed problems with a priori information /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Utrecht, The Netherlands :
VSP BV,
1995.
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| Colección: | Inverse and ill-posed problems series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Introduction""; ""CHAPTER 1. UNSTABLE PROBLEMS""; "" 1 Base formulations ofproblems""; ""1.1. Operator equations and systems""; ""1.2. The eigen-subspace determination of a linear operator""; "" 2 Ill-posed problems examples and its stability analysis""; ""2.1. The problem of gravimetry""; ""2.2. Integral equations in structure investigations of disorder materials""; ""2.3. The computerized tomography""; ""Â3 The classification of methods for unstable problems with a priori information""; ""3.1. Tikhonovâ€?s method""; ""3.2. The compact imbedding method""
- ""3.3. Linear iterative processes""""3.4. Î"-processes""; ""3.5. The descriptive regularization""; ""3.6. Iterative processes with quasi-contractions""; ""3.7. The iterative regularization method""; ""3.8. Combined methods""; ""3.9. Method of the regularization and penalties""; ""3.10. Methods of the mathematical programming""; ""CHAPTER 2. ITERATIVE METHODS FOR APPROXIMATION OF FIXED POINTS AND THEIR APPLICATION TO ILL-POSED PROBLEMS""; ""Â 1 Basic classes of mappings""; ""1.1. Quasi-nonexpansive and pseudo-contractive mappings""; ""1.2. Existence of fixed points""
- ""Â 2 Convergence theorems for iterative processes""""2.1. Strong convergence of iterations for quasi-contractions""; ""2.2. Weak convergence of iterations for pseudo-contractions""; ""Â 3 Iterations with correcting multipliers""; ""3.1. Stability of fixed points from parameter""; ""3.2. Strong iterative approximation of fixed points""; ""3.3. Generalization of results to quasi-nonexpansive operators""; ""Â 4 Applications to problems of mathematical programming""; ""4.1. Setting of a problem and definition of well-posedness""; ""4.2. Prox-algorithm for minimization of convex functional""
- ""4.3. Fejer processes for convex inequalities system""""4.4. Iterative processes for solution of operator equations with a priori information""; ""4.5. The gradient projection method for convex functional""; ""4.6. Minimization of quadratic functional""; ""Â 5 Regularizing properties of iterations""; ""5.1. Iterations with perturbed data and construction of regularizing algorithm""; ""5.2. Disturbance analysis for the Fejer processes""; ""5.3. Analysis of solution stability in the projection gradient method""; ""Â 6 Iterative processes with averaging""
- ""6.1. Formulation of the method and preliminary results""""6.2. The convergence theorem""; ""6.3. Stability with respect to perturbations. Weak regularization""; ""6.4. The Mann iterative processes""; ""Â 7 Iterative regularization of variational inequalities and of operator equations with monotone operators""; ""7.1. Formulation of problem""; ""7.2. The method of successive approximation in well-posed case""; ""7.3. Convergence of the iteratively regularized method of successive approximations""; ""7.4. Strong convergence of the Mann processes""