COMPLEXITY ESTIMATES FOR SEVERELY ILL-POSED PROBLEMS UNDER A POSTERIORI SELECTION OF REGULARIZATION PARAMETER
نویسندگان
چکیده
منابع مشابه
On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
In the study of the choice of the regularization parameter for Tikhonov regularization of nonlinear ill-posed problems, Scherzer, Engl and Kunisch proposed an a posteriori strategy in 1993. To prove the optimality of the strategy, they imposed many very restrictive conditions on the problem under consideration. Their results are difficult to apply to concrete problems since one can not make sur...
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In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing parameter choice methods, and evaluate...
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Straightforward solution of discrete ill-posed linear systems of equations or leastsquares problems with error-contaminated data does not, in general, give meaningful results, because propagated error destroys the computed solution. The problems have to be modified to reduce their sensitivity to the error in the data. The amount of modification is determined by a regularization parameter. It ca...
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We consider large scale ill-conditioned linear systems arising from discretization of ill-posed problems. Regularization is imposed through an (assumed known) upper bound constraint on the solution. An iterative scheme, requiring the computation of the smallest eigenvalue and corresponding eigenvector, is used to determine the proper level of regularization. In this paper we consider several co...
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ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2017
ISSN: 1392-6292,1648-3510
DOI: 10.3846/13926292.2017.1307284