Zero-ed initial guess to preconditioner for CG solver improves performance compared to using previous z

[elise-palethorpe]

I was having a play with preconditioning the CG solver with multigrid and found that I get considerably different results depending on whether I zero the initial guess to the preconditioner (see here). When the initial guess is all 0s the precondition! method is called ~1/3 of the number to times it is called if the given initial guess is used. My understanding is that the initial guess is not specified by the algorithm in fig 2.5 here so am not sure whether this is a "correct" answer here but would like to know why the zeroing gives such a different result. Could it be because solving for a residual equation the answer should be close to all 0s so it is actually a good initial guess?

cc @navidcy

[navidcy]

Seems like zeros is a better initial guess and thus #2654 does that.