Conjugate Gradient is widely used as a regularizing technique for solving linear systems with ill-conditioned coefficient matrix and right-hand side vector perturbed by noise. It enjoys a good convergence rate and computes quickly an iterate, say xkopt, which minimizes the error with respect to the exact solution. This behavior can be a disadvantage in the regulariza-tion context, because also the high-frequency components of the noise enter quickly the computed solution, leading to a difficult detection of kopt and to a sharp increase of the error after the koptth iteration. In this paper we propose an inner-outer algorithm based on a sequence of restarted Conjugate Gradients, with the aim of overcoming this drawback. A numerical experimentation validates the effectiveness of the proposed algorithm. ©2014 American Institute of Mathematical Sciences.
|Autori:||Favati P.; Lotti G.; Menchi O.; Romani F.|
|Titolo:||An inner-outer regularizing method for ill-posed problems|
|Anno del prodotto:||2014|
|Digital Object Identifier (DOI):||10.3934/ipi.2014.8.409|
|Appare nelle tipologie:||1.1 Articolo in rivista|