Separable nonlinear least squares: the variable projection method and its applications

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On approximation of functions by exponential sums (2005, background): “We refer to [13] for a good review of such approaches.”
Methodical fitting for mathematical models of rubber-like materials (2016, methodology): “Second, since the models contain only one non-linear term, we were also able to apply the VARPRO method devised by Golub and Pereyra (2003).”
Modelling stage—discharge relationships affected by hysteresis using the Jones formula and nonlinear regression (2006, background): “Henderson (1966) and Di Silvio (1969) allowed for diffusion by introducing parabolic and triangular approximations, respectively, to the flood wave in the Jones formula.”
Identification methods for Hammerstein nonlinear systems (2011, methodology): “Golub and Pereyra applied the projection method for solving separable nonlinear least squares problems [34].”
Load Modeling—A Review (2018, neutral): “Golub and Pereyra [116] proposed a variable projection based optimization algorithm to identify the parameters of several different load models.”