On the Existence of Nonsymmetric Matrices with Perfect Elimination Orderings

Permuting the rows and columns of a sparse matrix can dramatically reduce the memory requirements of a subsequently computed LU factorization. A perfect elimination matrix is one whose rows and columns can be permuted so that its LU factors require no additional space on top of that required by the original matrix. An implemention of an O(n) algorithm, presented in [6], for determining whether a matrix is perfect elimination is described. Running this code on 180 matrices from an assortment of application areas shows that 19 of them are perfect elimination and that almost half contain at least 40% eliminable entries.