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Journal of Applied Mathematics
Volume 2012, Article ID 312985, 12 pages
Research Article

Least Squares Problems with Absolute Quadratic Constraints

1Institute for Software Systems in Technical Appliations of Computer Science (FORWISS), University of Passau, InnstraBe 43, 94032 Passau, Germany
2Department of Mathematics and Computer Science, University of Passau, InnstraBe 43, 94032 Passau, Germany

Received 22 June 2011; Accepted 14 July 2011

Academic Editor: Juan Manuel Peña

Copyright © 2012 R. Schöne and T. Hanning. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.