On the Complexity of Sparse Gaussian Elimination via Bordering

The complexity of a general sparse Gaussian elimination algorithm based on the bordering algorithm is analyzed. It has been shown that this procedure requires less integer overhead storage than more traditional general sparse procedures, but the complexity of the nonnumerical overhead calculations was not clear. Here the nonnumerical complexity of the original procedure is shown to be comparable to the numerical complexity for an n× n grid graph, and an enhancement of the procedure that can reduce the overhead is presented.