Istituto di Informatica e Telematica     
Favati P., Lotti G., Menchi O., Romani F. An inner-outer regularizing method for ill-posed problems. In: Inverse Problems and Imaging, vol. 8 (2) pp. 409 - 420. American Institute of Mathematical Science (AIMS), 2014.
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.
Subject Regularization problems
iterative methods
conjugate gradient

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