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.
An inner-outer regularizing method for ill-posed problems
MENCHI, ORNELLA;ROMANI, FRANCESCO
2014-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
