I just saw a posting on Slashdot about how some researchers have found a way to speedup solving linear SDD systems. Here's a small excerpt:
Quote:
The result is a significant decrease in computer run times. The Gaussian elimination algorithm runs in time proportional to s^3, where s is the size of the SDD system as measured by the number of terms in the system, even when s is not much bigger than the number of variables. The new algorithm, by comparison, has a run time of s*[log(s)]^2. That means, if s = 1 million, that the new algorithm run time would be about a billion times faster than Gaussian elimination.

I wasn't sure if this applied to anyone writing matrix solvers for NFS or QS, but thought I'd mention it to see if it could help anyone.
You can find the Slashdot post here:
http://news.slashdot.org/story/10/10...arSDDSystems
The actual article from Carnegie Mellon University here:
http://www.cmu.edu/news/archive/2010...lgorithm.shtml
Or a pdf of the paper here:
http://www.cs.cmu.edu/~glmiller/Publ...ching2010.pdf