Geodesic
A full-Newton approach to separable nonlinear least squares problems and its application to discrete least squares rational approximation
Electronic transactions on numerical analysis, Tome 35 (2009), pp. 57-68.

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Summary: We consider a class of non-linear least squares problems that are widely used in fitting experimental data. A defining characteristic of the models we will consider is that the solution parameters may be separated into two classes, those that enter the problem linearly and those that enter non-linearly. Problems of this type are known as separable non-linear least squares (SNLLS) problems and are often solved using a Gauss-Newton algorithm that was developed in Golub and Pereyra [SIAM J. Numer. Anal., 10 (1973), pp. 413-432] and has been very widely applied.
Classification : 65F20, 65D10, 41A20
Keywords: separable nonlinear least squares, rational approximation 
@article{ETNA_2009__35__a12,
     author = {Borges, Carlos F.},
     title = {A {full-Newton} approach to separable nonlinear least squares problems and its application to discrete least squares rational approximation},
     journal = {Electronic transactions on numerical analysis},
     pages = {57--68},
     publisher = {mathdoc},
     volume = {35},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2009__35__a12/}
}
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Borges, Carlos F. A full-Newton approach to separable nonlinear least squares problems and its application to discrete least squares rational approximation. Electronic transactions on numerical analysis, Tome 35 (2009), pp. 57-68. http://geodesic.mathdoc.fr/item/ETNA_2009__35__a12/