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Non-linear fitting uses the least-squares criterion for goodness of fit, which is similar to linear regression. Non-linear fitting can also be expressed as a set of linear equations, but there is a substantive difference here since non-linear fitting is based on the idea of finding a set of parameters starting from an initial guess. The goal of non-linear fitting is to find the set of parameters that minimizes the least squares function. Thus, we can envision a multi-dimensional parameter space with each parameter contributing a dimension. One of the most common ways to minimize the function is to use the derivatives of the fitting function with respect to each of the parameters. These derivatives are slopes in the parameter space. The initial guess is important since one has to be close enough to the correct minimum that the derivatives will take the function down the correct path. If the guess is in the wrong "valley" in parameter space a non-sensical solution can be reached. It is a minimum, but it is far from the lowest or best minimum by the least squares criterion. The usual set of minimization methods can be employed in the process of finding the global minimum in the parameter space.
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