A discrepancy principle for Tikhonov regularization with approximately specified data
نویسندگان
چکیده
منابع مشابه
A Discrepancy Principle for Tikhonov Regularization with Approximately Specified Data
Many discrepancy principles are known for choosing the parameter in the regularized operator equation (T T + I)x = T y , ky ?y k , in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. In this paper we consider a class of discrepancy principles for choosing the regularization parameter when T T and T y are approximated by A n and z n respectively with ...
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In this paper severely ill-posed problems are studied which are represented in the form of linear operator equations with innnitely smoothing operators but with solutions having only a nite smoothness. It is well known, that the combination of Morozov's discrepancy principle and a nite dimensional version of the ordinary Tikhonov regularization is not always optimal because of its saturation pr...
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For solving linear ill-posed problems regularization methods are required when the right hand side and the operator are with some noise. In the present paper regularized solutions are obtained by Tikhonov regularization in Hilbert scales and the regularization parameter is chosen by the generalized discrepancy principle. Under certain smoothness assumptions we provide order optimal error bounds...
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In this paper, we consider the finite-dimensional approximations of Tikhonov regularization for nonlinear ill-posed problems with approximately given right-hand sides. We propose an a posteriori parameter choice strategy, which is a modified form of Morozov’s discrepancy principle, to choose the regularization parameter. Under certain assumptions on the nonlinear operator, we obtain the converg...
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In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minim...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1998
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-69-3-197-205