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Least squares problems with absolute quadratic constraints. (English) Zbl 1330.65099
Summary: 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.

MSC:
65K10 Numerical optimization and variational techniques
90C20 Quadratic programming
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