Minimizing a Non-linear Sum of Squares Function on a Small Computer

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Abstract
The Marquardt algorithm, by virtuc of its simplicity and reasonable convergence properties, has become a papular tool for minimising a sum of squares function. Doubts have been expressed in the literature, however, as to its efficiency and reliability when presented with pathological functions, and from these doubts more complicated algorithms have been synthesized. On a small computer algorithm complexity must if possible be avoided to conserve memory space, and under this constraint a compact implementation of the Marquardt algorithm has been developed which appears not to suffer from the failing this procedure has been reported to have. The moral of this history is that programming should be carried out with due care and attention to the nature of the problem at hand.

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