Least Squares Problems with Absolute Quadratic Constraints
R. Schöne, Tobias Hanning · Journal of Applied Mathematics · 2011
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.