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 (<a href="http:&#x2F;&#x2F;libelemental.org" rel="nofollow">http:&#x2F;&#x2F;libelemental.org</a>) use selective inversion of diagonal blocks to significantly improve their strong scalability.