Catálogo de publicaciones - tesis
Título de Acceso Abierto
Regularización de problemas inversos mal condicionados, calificación generalizada y saturación global
Karina Guadalupe Temperini Rubén Daniel Spies Pablo Miguel Jacovkis Domingo Alberto Tarzia Cristina Vilma Turner
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Resumen/Descripción – provisto por el repositorio digital
This Thesis includes the study of regularization methods for inverse ill-posed problems from a general point of view, using the spectral theory for linear operators in Hilbert spaces. A result of Thomas Seidman about the nonconvergence of least-squares method to the case of divergence of arbitrary speed was extended. The definition of qualification for spectral regularization methods introduced by Peter Mathé and Sergei Pereverzev in 2003 was also extended. Three levels of qualification were introduced: weak, strong and optimal. Necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification were provided. Implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems also were shown. A general theory of global saturation for arbitrary regularization methods was developed. Necessary and sufficient conditions for a method to have global saturation were provided and it was shown that in such methods the total error must be optimal in two precise ways. Converse results have been proved and the theory was applied to characterize saturation for spectral methods with classical and maximal qualification. The approximate inverse method was also used to develop regularization methods for solving inverse problems originated in concrete applications. Finally applications to inverse problems in heat conduction and image processing and numerical results allowing better visualization of the obtained theoretical results were presented.Palabras clave – provistas por el repositorio digital
Inverse ill-posed problems; Regularization methods; Qualification; Saturation; Least-squares method; Problemas inversos mal condicionados; Métodos de regularización; Calificación; Saturación; Método de mínimos cuadrados
Disponibilidad
| Institución detectada | Año de publicación | Navegá | Descargá | Solicitá |
|---|---|---|---|---|
| No requiere | 2008 | Biblioteca Virtual de la Universidad Nacional del Litoral (SNRD) |
|
Información
Tipo de recurso:
tesis
Idiomas de la publicación
- español castellano
País de edición
Argentina
Fecha de publicación
2008-03-10