[ODE] Choleski factorization

[david@csworkbench.com]

Well, I've given up on trying to get the last version of the iterated
algorithm to converge, so I'm back at Sergi's algorithm.  I was thinking
about ways to simplify the LCP solver for the single joint case, and I
came up with this idea:  Use a Cholesky factorization of the matrix A, and
solve once.  For each x that is outside of the bounds of lo and hi, clamp
it to that range, substitute into the original matrix, and subtract the
constants from the rhs.  Then resolve the remaining smaller problem.  My
question is, is a Cholesky Factorization also a factorization for all of
its sub-matrices?  Or maybe some combination of back- and
forward-substitution would make this work out?  Or would I have to
refactor it?  I'm hoping I can just skip over the columns that were
removed from the equation and get the correct solution, but If that
doesn't work, I could do a Gauss-Seidel iteration or two on it, unless
refactorization turns out to be just as fast by the time the iterative
scheme converges.  Of course, by the time I do 2 cholesky factorizations
and 2 solves, I've hardly sped up at all over LCP.

Thanks,
David