The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
Coleman, Thomas F.; Verma, Arun
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, bi-coloring, 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.
theory center; sparse Jacobian matrices; nonlinear systems of equations; nonlinear least squares; graph coloring; bi-coloring; automatic differentiation; computational differentiation; sparse finite differencing; partition problem; NP-complete problems; ADOL-C
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