Use of the P(4) and P(5) algorithms for in-core factorization of sparse matrices

We consider variants of the P?4 algorithm of Hel1erman and Rarick and the P?5 algorithm of Erisman, Grimes, Lewis and Poole, as used for generating a bordered block triangular form for the in-core solution of sparse sets of linear equations. We are particularly concerned with maintaining numerical stability and discuss methods for doing this and the extra cast that it entails. We also examine different factorization schemes, consider the use of matrix modification and iterative refinement, and compare the best variant with an established code for the solution of unsymmetric sparse sets of linear equations. We find that the established code is usualiy the most effective method.