Santhosh George, M. Thamban Nair, "An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 286147, 13 pages, 2003. https://doi.org/10.1155/S0161171203203197
An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales
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 , where 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 is a positive and selfadjoint operator. When the data 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).
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