Journal of Applied Mathematics

Least Squares Problems with Absolute Quadratic Constraints

R. Schöne and T. Hanning

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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.

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J. Appl. Math., Volume 2012 (2012), Article ID 312985, 12 pages.

First available in Project Euclid: 15 March 2012

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Schöne, R.; Hanning, T. Least Squares Problems with Absolute Quadratic Constraints. J. Appl. Math. 2012 (2012), Article ID 312985, 12 pages. doi:10.1155/2012/312985.

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