Generalized Cross-Validation applied to Conjugate Gradient for discrete ill-posed problems (Articolo in rivista)

Type
Label
  • Generalized Cross-Validation applied to Conjugate Gradient for discrete ill-posed problems (Articolo in rivista) (literal)
Anno
  • 2014-01-01T00:00:00+01:00 (literal)
Alternative label
  • P. Favati, G. Lotti, O. Menchi, F. Romani (2014)
    Generalized Cross-Validation applied to Conjugate Gradient for discrete ill-posed problems
    in Applied mathematics and computation
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • P. Favati, G. Lotti, O. Menchi, F. Romani (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 243 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 1 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • IIT-CNR, Dip. di Matematica, University of Parma, Dip. di Informatica, University of Pisa (literal)
Titolo
  • Generalized Cross-Validation applied to Conjugate Gradient for discrete ill-posed problems (literal)
Abstract
  • In this paper we propose a new method to apply the Generalized Cross-Validation (GCV) as a stopping rule for the Conjugate Gradient (CG). In general, to apply GCV to an iterative method, one must estimate the trace of the so-called influence matrix which appears in the denominator of the GCV function. In the case of CG, unlike what happens with stationary iterative methods, the regularized solution has a nonlinear dependence on the noise which affects the data of the problem. This fact is often pointed out as a cause of poor performance of GCV. To overcome this drawback, our proposal linearizes the dependence by computing the derivatives through iterative formulas. We compare the proposed method with other methods suggested in the literature by an extensive numerical experimentation on both 1D and 2D test problems. (literal)
Prodotto di
Autore CNR

Incoming links:


Prodotto
Autore CNR di
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#rivistaDi
data.CNR.it