Computing Large Sparse Jacobian Matrices Using Automatic Differentiation

The computation of large sparse Jacobian matrices is required in many important large-scale scientific problems. Three approaches to computing such matrices are considered: hand-coding, difference approximations, and automatic differentiation using the ADIFOR (automatic differentiation in Fortran) tool. The authors compare the numerical reliability and computational efficiency of these approaches on applications from the MINPACK-2 test problem collection. The conclusion is that ADIFOR is the method of choice, leading to results that are as accurate as hand-coded derivatives, while at the same time outperforming difference approximations in both accuracy and speed.