A trust region method for implicit orthogonal distance regression (Q1315240)

The authors are interested in the construction of a trust region for implicit orthogonal distance regression for curves or surfaces given in implicit form via the model equation \(f(x,\beta)=0\), where \(x\in R^ d\) and \(\beta\in R^ m\). The algorithm for solving the problem to find a parameter vector \(\beta^*\) such that the contour \(f(x,\beta^*)=0\) is a best fit for a given data \(z_ i\), \(i=1,\dots,n\), in a least squares sense, is presented. Comparison with the algorithm of \textit{H. I. Britt} and \textit{R. H. Luecke} [Technometrics 15, 233-247 (1973; Zbl 0257.62041)] is done and the method is illustrated on the example.