We first describe some experiments in using MA57, an HSL multifrontal code for symmetric indefinite systems, to detect the rank of highly deficient rectangular systems. The application of interest was in limit analysis problems from Geotechnical Engineering and was conducted jointly with Scott Sloan and Andrei Lyamin from the University of Newcastle, NSW. We discuss algorithmic changes that were needed in MA57 and compare our strategy with using a modified version of the HSL code MA48 directly on the rectangular system. The use of this code for saddle-point (KKT) matrices will be discussed.

We have also developed a multifrontal code for skew symmetric systems using a modified version of the pivoting strategy developed by Duff, Gilbert, and Pralet that works on a reduced matrix. It is interesting that the skew solver is much simpler than its counterpart for symmetric indefinite systems. We show results from a prototype code and discus the uses of such a solver.