The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
Thomas F. Coleman, Arun Verma · SIAM Journal on Scientific Computing · 1998
This paper is concerned with the efficient computation of sparse Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of a graph coloring technique, bicoloring, to exploit the sparsity of the Jacobian matrix J and thereby allow for the efficient determination of J using AD software. We analyze both a direct scheme and a substitution process. We discuss the results of numerical experiments indicating significant practical potential of this approach.