Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of the regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. This paper provides an analysis of iterated Tikhonov regularization with a regularization matrix different from the identity. Computed examples illustrate the performance of this method.

Iterated Tikhonov regularization with a general penalty term

Buccini A.;Donatelli M.;Reichel L.
2017-01-01

Abstract

Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of the regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. This paper provides an analysis of iterated Tikhonov regularization with a regularization matrix different from the identity. Computed examples illustrate the performance of this method.
2017
Ill-conditioned discrete problem; Ill-posed problem; Iterative regularization method; Tikhonov regularization
File in questo prodotto:
File Dimensione Formato  
GIT.pdf

Solo gestori archivio

Tipologia: versione post-print
Dimensione 443.24 kB
Formato Adobe PDF
443.24 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/278194
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 37
  • ???jsp.display-item.citation.isi??? 36
social impact