Preconditioning techniques for linear systems are widely used in order to speed up the convergence of iterative methods. If the linear system is generated by the discretization of an ill-posed problem, preconditioning may lead to wrong results, since components related to noise on input data are amplified. Using basic concepts from the theory of inverse problems, we identify a class of preconditioners which acts as a regularizing tool. In this paper we study relationships between this class and previously known circulant preconditioners for ill-conditioned Hermitian Toeplitz systems. In particular, we deal with the low-pass filtered optimal preconditioners and with a recent family of superoptimal preconditioners. We go on to describe a set of preconditioners endowed with particular regularization properties, whose effectiveness is supported by several numerical tests. © 2004 Elsevier Inc. All rights reserved.
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|Titolo:||A classification scheme for regularizing preconditioners, with application to Toeplitz systems|
|Data di pubblicazione:||2005|
|Appare nelle tipologie:||01.01 - Articolo su rivista|