Block Triangular Orderings 1 Block Triangular Orderings and Factors for SparseMatrices in

Sparse matrix methods for factorizing a nonsingular matrix are considered. The possibility of using the little known technique of implicit LU factors is explored, particularly in the context of simplex-like methods for Linear Programming. The concept of a spike-preserving ordering is introduced and a new method for calculating such an ordering is described, based on the recursive use of Tarjan's algorithm for block triangularization. Experiments are described in which the new method is compared to that based on the use of Markowitz orderings.