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An inner-outer regularizing method for ill-posed problems

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 x_{kopt}, which minimizes the error with respect to the exact solution. This behavior can be a disadvantage in the regularization 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 kopt-th 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.


Inverse Problems and Imaging, 2014

Autori esterni: Grazia Lotti (Dip. di Matematica, University of Parma, Parma, Italy), Ornella Menchi (Dip. di Informatica, University of Pisa, Pisa, Italy), Francesco Romani (Dip. di Informatica, University of Pisa, Pisa, Italy)
Autori IIT:

Tipo: Articoli su riviste ISI
Area di disciplina: Mathematics
Da pagina 409 a pagina 420

Attività: Metodi numerici per problemi di grandi dimensioni