Journal of Applied Mathematics

Least Squares Problems with Absolute Quadratic Constraints

R. Schöne and T. Hanning

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331817617

Digital Object Identifier
doi:10.1155/2012/312985

Mathematical Reviews number (MathSciNet)
MR2830978

Zentralblatt MATH identifier
1330.65099

Citation

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. https://projecteuclid.org/euclid.jam/1331817617


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