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ACM Transactions on Mathematical Software (TOMS)
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ACM Transactions on Mathematical Software (TOMS)
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ACM Transactions on Mathematical Software (TOMS)
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ACM Transactions on Mathematical Software (TOMS)
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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.