Least Squares Problems with Absolute Quadratic Constraints
This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be d...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/312985 |
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| _version_ | 1832548142604615680 |
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| author | R. Schöne T. Hanning |
| author_facet | R. Schöne T. Hanning |
| author_sort | R. Schöne |
| collection | DOAJ |
| description | This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented. |
| format | Article |
| id | doaj-art-aeec24ddce384f4d8908928bbc335ddd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-aeec24ddce384f4d8908928bbc335ddd2025-02-03T06:42:02ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/312985312985Least Squares Problems with Absolute Quadratic ConstraintsR. Schöne0T. Hanning1Institute for Software Systems in Technical Appliations of Computer Science (FORWISS), University of Passau, InnstraBe 43, 94032 Passau, GermanyDepartment of Mathematics and Computer Science, University of Passau, InnstraBe 43, 94032 Passau, GermanyThis paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.http://dx.doi.org/10.1155/2012/312985 |
| spellingShingle | R. Schöne T. Hanning Least Squares Problems with Absolute Quadratic Constraints Journal of Applied Mathematics |
| title | Least Squares Problems with Absolute Quadratic Constraints |
| title_full | Least Squares Problems with Absolute Quadratic Constraints |
| title_fullStr | Least Squares Problems with Absolute Quadratic Constraints |
| title_full_unstemmed | Least Squares Problems with Absolute Quadratic Constraints |
| title_short | Least Squares Problems with Absolute Quadratic Constraints |
| title_sort | least squares problems with absolute quadratic constraints |
| url | http://dx.doi.org/10.1155/2012/312985 |
| work_keys_str_mv | AT rschone leastsquaresproblemswithabsolutequadraticconstraints AT thanning leastsquaresproblemswithabsolutequadraticconstraints |