Geodesic
On Krylov projection methods and Tikhonov regularization
Electronic transactions on numerical analysis, Tome 44 (2015), pp. 83-123
In the framework of large-scale linear discrete ill-posed problems, Krylov projection methods represent an essential tool since their development, which dates back to the early 1950's. In recent years, the use of these methods in a hybrid fashion or to solve Tikhonov regularized problems has received great attention especially for problems involving the restoration of digital images. In this paper we review the fundamental Krylov-Tikhonov techniques based on Lanczos bidiagonalization and the Arnoldi algorithms. Moreover, we study the use of the unsymmetric Lanczos process that, to the best of our knowledge, has just marginally been considered in this setting. Many numerical experiments and comparisons of different methods are presented.
Classification : 65F10, 65F22, 65R32
Keywords: discrete ill-posed problems, Krylov projection methods, Tikhonov regularization, Lanczos bidiagonalization, nonsymmetric Lanczos process, arnoldi algorithm, discrepancy principle, generalized cross validation, L-curve criterion, regińska criterion, image deblurring 
@article{ETNA_2015__44__a25,
     author = {Gazzola,  Silvia and Novati,  Paolo and Russo,  Maria Rosaria},
     title = {On {Krylov} projection methods and {Tikhonov} regularization},
     journal = {Electronic transactions on numerical analysis},
     pages = {83--123},
     year = {2015},
     volume = {44},
     zbl = {1312.65065},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__44__a25/}
}
TY  - JOUR
AU  - Gazzola,  Silvia
AU  - Novati,  Paolo
AU  - Russo,  Maria Rosaria
TI  - On Krylov projection methods and Tikhonov regularization
JO  - Electronic transactions on numerical analysis
PY  - 2015
SP  - 83
EP  - 123
VL  - 44
UR  - http://geodesic.mathdoc.fr/item/ETNA_2015__44__a25/
LA  - en
ID  - ETNA_2015__44__a25
ER  - 
%0 Journal Article
%A Gazzola,  Silvia
%A Novati,  Paolo
%A Russo,  Maria Rosaria
%T On Krylov projection methods and Tikhonov regularization
%J Electronic transactions on numerical analysis
%D 2015
%P 83-123
%V 44
%U http://geodesic.mathdoc.fr/item/ETNA_2015__44__a25/
%G en
%F ETNA_2015__44__a25
Gazzola,  Silvia; Novati,  Paolo; Russo,  Maria Rosaria. On Krylov projection methods and Tikhonov regularization. Electronic transactions on numerical analysis, Tome 44 (2015), pp. 83-123. http://geodesic.mathdoc.fr/item/ETNA_2015__44__a25/