[18335fall09] pset 5 problem 3 comment

[Steven G. Johnson]

On problem 3, where you use the CG algorithm to find a nullspace  
vector of a semidefinite matrix, you will probably find that something  
odd happens: it converges to something with a small residual ||Ax|| /  
||x||, but then if you keep doing iterations after that the residual  
goes crazy and starts increasing again, due to roundoff errors I think.

This is okay.  In practice, you would usually just stop the iteration  
when the residual becomes sufficiently small.

Alternatively, I think that there are probably ways to slightly  
rearrange the algorithm to eliminate the sensitivity to roundoff  
errors once the residual gets small.  (For example, just restarting CG  
once the residual is small seems to work somewhat.)  But you don't  
need to do this for your solutions.

--SGJ