A simple implementation in R of the Gauss-Newton algorithm, the iterative optimization algorithm is applied to the small Chwirut1 dataset.
The dataset is a collection of 214 observations acquired for a study involving ultrasonic calibration and can be downloaded from http://www.itl.nist.gov/div898/strd/nls/data/LINKS/DATA/Chwirut1.dat
Fit model in red: