An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales

Santhosh George and M. Thamban Nair

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-13

Abstract:

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 T x = 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 Hilbert scales, when T is a positive and selfadjoint operator. When the data y is known only approximately, our method provides optimal order under certain natural assumptions on the ill-posedness of the equation and smoothness of the solution. The result, in fact, improves an earlier work of the authors (1997).

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:286147

DOI: 10.1155/S0161171203203197

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