A Method for Computing Initial Approximations for a 3-parameter Exponential Function

This paper proposes a modified method (MM) for computing initial guess values (IGVs) of a single exponential class of transcendental least square problems. The proposed method is an improvement of the already published multiple goal function (MGF) method. Current approaches like the Gauss-Newton, Maximum likelihood, Levenberg-Marquardt etc. methods for computing parameters of transcendental least squares models use iteration routines that require IGVs to start the iteration process. According to reviewed literature, there is no known documented methodological procedure for computing the IGVs. It is more of an art than a science to provide a “good” guess that will guarantee convergence and reduce computation time.

To evaluate the accuracy of the MM method against the existing Levenberg-Marquardt (LM) and the MGF methods, numerical studies are examined on the basis of two problems that’s; the growth and decay processes. The mean absolute percentage error (MAPE) is used as the measure of accuracy among the methods. Results show that the modified method achieves higher accuracy than the LM and MGF methods and is computationally attractive. However, the LM method will always converge to the required solution given “good” initial values.

The MM method can be used to compute estimates for IGVs, for a wider range of existing methods of solution that use iterative techniques to converge to the required solutions.