Abstract
Gaussian elimination is studied as the elimination process in the bipartite graph associated with the matrix of the system, and the concept of reachable sets applied to bipartite graphs is introduced. A characterization of the elimination graphs in terms of reachable sets is presented for the case of bipartite graphs. A bipartite quotient graph model is given, which allows the computation of reachable sets during the elimination process in a more advantageous way. An implementation of the bipartite quotient graph model as well as the advantages of applying quotient graphs over elimination graphs are considered. This extends to the unsymmetric case the theory of George and Liu (5).
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