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In this paper, we describe ODRPACK, a software package for the weighted orthogonal distance regression problem. This software is an implementation of the algorithm described in 2 for finding the parameters that minimize the sum of the squared weighted orthogonal distances from a set of observations to a curve or surface determined by the parameters. It can also be used to solve the ordinary nonlinear least squares problem. The weighted orthogonal distance regression procedure application to curve and surface fitting and to measurement error models in statistics. The algorithm implemented is an efficient and stable trust region (Levenberg-Marquardt) procedure that exploits the structure of the problem so that the computational cost per iteration is equal to that for the same type of algorithm applied to the ordinary nonlinear least squares problem. The package allows a general weighting scheme, provides for finite difference derivatives, and contains extensive error checking and report generating facilities.
Boggs et al. (Fri,) studied this question.