Trust-region and other regularisations of linear least-squares problems
We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x|| ≤ Δ is imposed on the size of the solution, and in which the least value of linear combinations of |...
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| Format: | Report |
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Unspecified
2008
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| _version_ | 1826264357794742272 |
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| author | Cartis, C Gould, N Toint, P |
| author_facet | Cartis, C Gould, N Toint, P |
| author_sort | Cartis, C |
| collection | OXFORD |
| description | We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x|| ≤ Δ is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax-b||2q and a regularisation term ||x||2p for various p and q=1,2 is sought. In each case, one of more "secular" equations are derived, and fast Newton-like solution procedures are suggested. The resulting algorithms are available as part of the GALAHAD optimization library. |
| first_indexed | 2024-03-06T20:06:30Z |
| format | Report |
| id | oxford-uuid:291499c3-ea51-49b1-9c48-7c6becf001d7 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:06:30Z |
| publishDate | 2008 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:291499c3-ea51-49b1-9c48-7c6becf001d72022-03-26T12:16:53ZTrust-region and other regularisations of linear least-squares problemsReporthttp://purl.org/coar/resource_type/c_93fcuuid:291499c3-ea51-49b1-9c48-7c6becf001d7Mathematical Institute - ePrintsUnspecified2008Cartis, CGould, NToint, PWe consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x|| ≤ Δ is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax-b||2q and a regularisation term ||x||2p for various p and q=1,2 is sought. In each case, one of more "secular" equations are derived, and fast Newton-like solution procedures are suggested. The resulting algorithms are available as part of the GALAHAD optimization library. |
| spellingShingle | Cartis, C Gould, N Toint, P Trust-region and other regularisations of linear least-squares problems |
| title | Trust-region and other regularisations of linear least-squares problems |
| title_full | Trust-region and other regularisations of linear least-squares problems |
| title_fullStr | Trust-region and other regularisations of linear least-squares problems |
| title_full_unstemmed | Trust-region and other regularisations of linear least-squares problems |
| title_short | Trust-region and other regularisations of linear least-squares problems |
| title_sort | trust region and other regularisations of linear least squares problems |
| work_keys_str_mv | AT cartisc trustregionandotherregularisationsoflinearleastsquaresproblems AT gouldn trustregionandotherregularisationsoflinearleastsquaresproblems AT tointp trustregionandotherregularisationsoflinearleastsquaresproblems |