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The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation

Author
Coleman, Thomas F.; Verma, Arun
Abstract
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.
Date Issued
1995-12Publisher
Cornell University
Subject
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
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/95-225
Type
technical report