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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| Format: | Article |
| Language: | English |
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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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| author | Santhosh George M. Thamban Nair |
| author_facet | Santhosh George M. Thamban Nair |
| author_sort | Santhosh George |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-14ea7c9b3f1640349689ebadda6a2fd0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-14ea7c9b3f1640349689ebadda6a2fd02025-02-03T05:52:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003392487249910.1155/S0161171203203197An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scalesSanthosh George0M. Thamban Nair1Department of Mathematics, Government College, Sanquelim, Goa 403505, IndiaDepartment of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, IndiaRecently, 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).http://dx.doi.org/10.1155/S0161171203203197 |
| spellingShingle | 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 |
| title | An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales |
| title_full | An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales |
| title_fullStr | An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales |
| title_full_unstemmed | An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales |
| title_short | An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales |
| title_sort | optimal order yielding discrepancy principle for simplified regularization of ill posed problems in hilbert scales |
| url | http://dx.doi.org/10.1155/S0161171203203197 |
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