Computing Large Sparse Jacobian Matrices Using Automatic Differentiation

The computation of large sparse Jacobian matrices is required in many important large-scale scientific problems. We consider three approaches to computing such matrices: hand-coding, difference approximations, and automatic differentiation using the ADIFOR (Automatic Differentiation in Fortran) tool. We compare the numerical reliability and computational efficiency of these approaches on applications from the MINPACK-2 test problem collection. Our conclusion is that automatic differentiation 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. COMPUTING LARGE SPARSE JACOBIAN MATRICES USING AUTOMATIC DIFFERENTIATION Brett M. Averick , Jorge J. Mor'e, Christian H. Bischof, Alan Carle , and Andreas Griewank 1 Introduction The solution of large-scale nonlinear problems often requires the computation of the Jacobian matrix f 0 (x) of a mapping f : IR ..