NDLI: A new framework for multi-parameter regularization

Content Provider	Springer Nature Link
Author	Reichel, Lothar Gazzola, Silvia
Copyright Year	2015
Abstract	This paper proposes a new approach for choosing the regularization parameters in multi-parameter regularization methods when applied to approximate the solution of linear discrete ill-posed problems. We consider both direct methods, such as Tikhonov regularization with two or more regularization terms, and iterative methods based on the projection of a Tikhonov-regularized problem onto Krylov subspaces of increasing dimension. The latter methods regularize by choosing appropriate regularization terms and the dimension of the Krylov subspace. Our investigation focuses on selecting a proper set of regularization parameters that satisfies the discrepancy principle and maximizes a suitable quantity, whose size reflects the quality of the computed approximate solution. Theoretical results are shown and illustrated by numerical experiments.
Ending Page	949
Page Count	31
Starting Page	919
File Format	PDF
ISSN	00063835
e-ISSN	15729125
Journal	BIT Numerical Mathematics
Issue Number	3
Volume Number	56
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-12-16
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Arnoldi–Tikhonov method Ill-posed problems Computational Mathematics and Numerical Analysis Discrepancy principle Inverse problems Iterative methods for linear systems Numeric Computing Multi-parameter Tikhonov method Mathematics Ill-posedness, regularization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Networks and Communications Computational Mathematics Software

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