Gauss–Newton algorithm

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In numerical methods, the Gauss–Newton algorithm is an iterative algorithm to solve non-linear least squares problems. It is an extension of Newton's method for finding a minimum of a sum of squared functions. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method to iteratively approximate zeroes of the components of the sum, and thus minimizing the sum. In this sense, the algorithm is also an effective method for solving overdetermined systems of equations. It has the advantage that second derivatives, which can be challenging to compute, are not required. Non-linear least squares problems arise, for instance, in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations. The method is named after the mathematicians Carl Friedrich Gauss and Isaac Newton, and first appeared in Gauss's 1809 work Theoria motus corporum coelestium in sectionibus conicis solem ambientum.

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