Experiments in tearing large sparse systems

If one removes some variables and equations from a large sparse system of linear equations, the resulting subsystem may have characteristics which render it amenable to rapid and economic solution. There are men various methods for obtaining a solution to the original system. This class of techniques is often termed 'tearing' and has been widely used in several application areas including linear programming, chemical engineering, and economic modelling. Many tearing algorithms give a matrix which can be partitioned as a block triangular fonn. We discuss algorithms and software for obtaining this form, comment on some stability issues, and consider implications for the solution of large sparse sets of linear equations.