Estimate of the number of arithmetic operations required in the LU decomposition of a sparse matrix

The expected number of arithmetic operations required to compute the table of factors in the LU decomposition of an nth-order sparse symmetric incidence matrix is shown to increase quadratically with the number of branches incident at any node, but only linearly with the number of nodes. This same result is observed if the sparse incidence matrix is symmetric only in pattern. It is assumed that the same number of branches is incident at every node and that the nodes are ordered randomly.