Least squares problems with absolute quadratic constraints.

*(English)*Zbl 1330.65099Summary: 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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\textit{R. Schöne} and \textit{T. Hanning}, J. Appl. Math. 2012, Article ID 312985, 12 p. (2012; Zbl 1330.65099)

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