On Wed, Jun 4, 2014 at 7:21 AM, Thomas Covert <[email protected]> wrote: > Your code is about twice as fast (when N = 1000) as the code I initially > posted. I think the speed gains come from the fact that your code does all > its work on real numbers, so it only has to do one floating point operation > per operation, while my "choldn" works directly on DualNumbers. Still, it > would be great if there was a smart LAPACK routine to do the "Sylvester > Equation" step as fast as the other standard back substitution routines.
I didn't find anything which solves the problem while fully exploiting the available structure, but I think the version I've put in the pull request here https://github.com/scidom/DualNumbers.jl/pull/11 should be pretty good efficiency wise since the heavy lifting basically gets handed off to gemv calls. It is basically a forward substitution, but exploiting the structure is important because the underlying linear system is quite sparse. Did you end up using this in the end, or did you find a better way to formulate the problem? ~Chris
