I came here to cite the same paper, but your comment about efficiency is only true in a limited context. Applying an explicitly-computed inverse exposes more p

I came here to cite the same paper, but your comment about efficiency is only true in a limited context. Applying an explicitly-computed inverse exposes more parallelism than solving with factors. State of the art parallel linear algebra packages like Elemental (http://libelemental.org http://libelemental.org) use selective inversion of diagonal blocks to significantly improve their strong scalability.