Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations
Simplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the no...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306095 |
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| author | Santhosh George M. Thamban Nair |
| author_facet | Santhosh George M. Thamban Nair |
| author_sort | Santhosh George |
| collection | DOAJ |
| description | Simplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with respect to certain natural assumptions on the ill posedness of the equation. The results are shown to be applicable to a wide class of spline approximations in the setting of Sobolev scales. |
| format | Article |
| id | doaj-art-3b8ab626702f4169a5f2ee31fa328ba9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3b8ab626702f4169a5f2ee31fa328ba92025-02-03T01:03:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004371973199610.1155/S0161171204306095Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizationsSanthosh George0M. Thamban Nair1Department of Mathematics, Government College of Arts, Science and Commerce, Sanquelim, Goa 403505, IndiaDepartment of Mathematics, Indian Institute of Technology Madras, Chennai 600036, IndiaSimplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with respect to certain natural assumptions on the ill posedness of the equation. The results are shown to be applicable to a wide class of spline approximations in the setting of Sobolev scales.http://dx.doi.org/10.1155/S0161171204306095 |
| spellingShingle | Santhosh George M. Thamban Nair Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations International Journal of Mathematics and Mathematical Sciences |
| title | Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations |
| title_full | Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations |
| title_fullStr | Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations |
| title_full_unstemmed | Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations |
| title_short | Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations |
| title_sort | optimal order yielding discrepancy principle for simplified regularization in hilbert scales finite dimensional realizations |
| url | http://dx.doi.org/10.1155/S0161171204306095 |
| work_keys_str_mv | AT santhoshgeorge optimalorderyieldingdiscrepancyprincipleforsimplifiedregularizationinhilbertscalesfinitedimensionalrealizations AT mthambannair optimalorderyieldingdiscrepancyprincipleforsimplifiedregularizationinhilbertscalesfinitedimensionalrealizations |