Computing Large Sparse Jacobian Matrices Using Automatic Differentiation

The computation of large sparse Jacobian matrices is required in many important large-scale scienti c problems. We consider three approaches to computing such matrices: hand-coding, di erence approximations, and automatic di erentiation using the ADIFOR (Automatic Di erentiation in Fortran) tool. We compare the numerical reliability and computational e ciency of these approaches on applications from the MINPACK-2 test problem collection. Our conclusion is that automatic di erentiation is the method of choice, leading to results that are as accurate as hand-coded derivatives, while at the same time outperforming di erence approximations in both accuracy and speed. COMPUTING LARGE SPARSE JACOBIAN MATRICES USING AUTOMATIC DIFFERENTIATION Brett M. Averick , Jorge J. Mor e, Christian H. Bischof, Alan Carle , and Andreas Griewank