• Journal of Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.407-416
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• 1998

For fast Cholesky factorization, it is most important to reduce the number of nonzero elements by ordering methods. Generally, the minimum deficiency ordering produces less nonzero elements, but it is very slow. We propose an efficient implementation method. The minimum deficiency ordering requires much computations related to adjacent nodes. But, we reduce those computations by using indistinguishable nodes, the clique storage structures, and the explicit storage structures to compute deficiencies.

• Korean Management Science Review
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• v.12 no.2
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• pp.31-42
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• 1995

The ordering method is used to reduce the fill-ins in interior point methods. In ordering, the data structure plays an important role. In this paper, first, we compare the efficiency and the memory storage requirement of the quotient graph structure and the clique storage. Next, we propose a method of reducing the number of cliques and a data structure for clique storage. Finally, we apply a method of merging rows and absorbing cliques and show the experimental results.