Solving Parametric Sparse Linear Systems by Local Blocking, II

The present author, Inaba and Kako proposed local blocking in a recent paper [6], for solving parametric sparse linear systems appearing in industry, so that the obtained solution is suited for determining optimal parameter values. They employed a graph theoretical treatment, and the points of their method are to select strongly connected subgraphs satisfying several restrictions and to form the so-called "characteristic system". The method of selecting subgraphs is, however, complicated and seems to be unsuited for big systems. In this paper, assuming that a small number of representative vertices of the characteristic system are specified by the user, we give a simple method of finding a characteristic system. Then, we present a simple and satisfactory method of decomposing the given graph into strongly connected subgraphs. The method applies the SCC (strongly connected component) decomposition algorithm. The complexity of new method is O(#(vertex) +#(edge)). We test our method successfully by three graphs of 100 vertices made artificially showing different but typical features.