The completely random system

This is a system with non-zeros spread uniformly all over. The system is quite sparse (only $17.38\%$ non-zeros), but there is no obvious ``better ordering''. The result from the optimization is expected to show little improvement, but is nonetheless interesting due to the difficult nature of the system.

Figure 7.1: The completely random system. $nz = 17.38\%$

As expected, the optimization didn't improve the structure of the system much. In figure 7.2, the optimized system is shown, along with the resulting R matrix. The R matrix is almost dense, indicating that fill-ins have been generated heavily throughout the system.

Figure 7.2: Ordered ``random'' system before and after QR

Solver	KFLOPS
MatLab	351.2
QR	140.8