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 Tx=y, where T is a bounded linear operator between Hilbert spaces. Motivated by th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203203197 |
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| Summary: | 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 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). |
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| ISSN: | 0161-1712 1687-0425 |