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

The Marquardt algorithm, by virtuc of its simplicity and reasonableconvergence properties, has become a papular tool for minimisinga sum of squares function. Doubts have been expressed in theliterature, however, as to its efficiency and reliability whenpresented with pathological functions, and from these doubtsmore complicated algorithms have been synthesized. On a smallcomputer algorithm complexity must if possible be avoided toconserve memory space, and under this constraint a compact implementationof the Marquardt algorithm has been developed which appearsnot to suffer from the failing this procedure has been reportedto have. The moral of this history is that programming shouldbe carried out with due care and attention to the nature ofthe problem at hand.