1) For standard non-linear least squares, the standard approaches are to either a) to use the jacobian to linearize, and proceed with linear regression, or to b) linearize the raw data 2) When data needs to be "fit" to a complicated model (e.g. some non-linear differential equation) that has no closed form analytic solution, people typically run a simulation varying the model parameters until the least squares residuals is minimized. Fit parameter distributions are then estimated using monte carlo boostrap, or a polynomial approximation in the vicinity of the residual least squares minimum. Has anyone here seen any literature about linearizing the data for case 2 and fitting with a difference equation approximation for the non-linear dif. e.q. ? For example let's say our data is described by y = A*exp(-t/tau)+c. The y data can be linearized by with a time difference approximation y(t+1)-y(t)/dt = -y(t)/tau. and the equation above can be use to fit it. This technique would also apply to more complicated non-linear diffy q's so long they can represented as difference equations.