Markowitz-type heuristics for computing Jacobian matrices efficiently

Authors:
Andreas Albrecht;Peter Gottschling;Uwe Naumann
Affiliations:
Department of Computer Science, University of Hertfordshire;Department of Computer Science, University of Hertfordshire;Mathematics and Computer Science Division, Argonne National Laboratory
Venue:
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
Year:
2003

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Abstract

We consider the problem of accumulating the Jacobian matrix of a nonlinear vector function by using a minimal number of arithmetic operations. Two new Markowitz-type heuristics are proposed for vertex elimination in linearized computational graphs, and their superiority over existing approaches is shown by several tests. Similar ideas are applied to derive new heuristics for edge elimination techniques. The well known superiority of edge over vertex elimination can be observed only partially for the heuristics discussed in this paper. Nevertheless, significant improvements can be achieved by the new heuristics both in terms of the quality of the results and their robustness with respect to different tiebreaking criteria.