A Comparison of Several Methods of Solving Nonlinear Regression Groundwater Flow Problems

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear‐regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi‐linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi‐Newton method, and last was the Fletcher‐Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher‐Reeves method, and this was followed closely by the quasi‐Newton method. The Marquardt and quasi‐linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi‐linearization methods than for the other two. Hence the quasi‐Newton (and perhaps Fletcher‐Reeves) method might be more efficient than either the Marquardt or quasi‐linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi‐linearization metilod for three of the four problems. For all four problems the quasi‐Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher‐Reeves method required slightly less memory than the quasi‐Newton method. Memory requirements were not excessive for any of the four methods.