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High Quality Content by WIKIPEDIA articles! Non-linear least squares is the form of least squares analysis which is used to fit a set of m observations with a model that is non-linear in n unknown parameters (m n). It is used in some forms of non-linear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences. The more the parameter values differ from their optimal values, the more the contours deviate from elliptical shape. A consequence of this is that initial parameter estimates should be as close as practicable to their (unknown!) optimal values. It also explains how divergence can come about as the Gauss-Newton algorithm is convergent only when the objective function is approximately quadratic in the parameters.