Premium
Iterated Tikhonov regularization with a general penalty term
Author(s) -
Buccini Alessandro,
Donatelli Marco,
Reichel Lothar
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2089
Subject(s) - tikhonov regularization , regularization perspectives on support vector machines , backus–gilbert method , regularization (linguistics) , mathematics , iterated function , identity matrix , proximal gradient methods for learning , zeta function regularization , mathematical optimization , mathematical analysis , inverse problem , computer science , artificial intelligence , eigenvalues and eigenvectors , physics , quantum mechanics , prime zeta function , arithmetic zeta function , riemann hypothesis
Summary 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.