On the generalized discrepancy principle for Tikhonov regularization in Hilbert scales
نویسندگان
چکیده
منابع مشابه
On the Generalized Discrepancy Principle for Tikhonov Regularization in Hilbert Scales
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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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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Recently, Tautenhahn and Hämarik (1999) have considered a monotone rule as a parameter choice strategy for choosing the regularization parameter while considering approximate solution of an ill-posed operator equation Tx =y , where T is a bounded linear operator between Hilbert spaces. Motivated by this, we propose a new discrepancy principle for the simplified regularization, in the setting of...
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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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ژورنال
عنوان ژورنال: Journal of Integral Equations and Applications
سال: 2010
ISSN: 0897-3962
DOI: 10.1216/jie-2010-22-3-483