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Title: The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
Authors: Coleman, Thomas F.
Verma, Arun
Keywords: theory center
sparse Jacobian matrices
nonlinear systems of equations
nonlinear least squares
graph coloring
automatic differentiation
computational differentiation
sparse finite differencing
partition problem
NP-complete problems
Issue Date: Dec-1995
Publisher: Cornell University
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.
Appears in Collections:Cornell Theory Center Technical Reports

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