Computing a sparse Jacobian matrix by rows and columns
A.K.M. Shahadat Hossain and Trond Steihaug
Reports in Informatics No. 109, October 1995, Department of
Informatics, University of Bergen, Norway.
Abstract
Efficient estimation of large sparse Jacobian matrices has been
studied extensively in the last couple of years. It has been observed
that the estimation of Jacobian matrix can be posed as a graph
coloring problem. Elements of the matrix are estimated by taking
divided difference in several directions corresponding to a group of
structurally independent columns. Another possibility is to obtain
the nonzero elements by means of the so called Automatic
differentiation (AD), which gives the estimates free of truncation
error that one encounters in a divided difference scheme. In this
paper we show that it is possible to exploit sparsity both in columns
and rows by employing the forward and the reverse mode of Automatic
differentiation. A graph-theoretic characterization of the problem is
given.
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