Standardize iterators/reset! functionality, iterative "factorizations"

[jagot]

Related to #166

I think it would be nice if the various solvers had the same interface to create iterators (which would reduce the amount of boilerplate in e.g. https://github.com/haampie/JacobiDavidson.jl to support different solvers).

If we could also have a reset! function to set new right-hand-sides and reinitialize all helper structures as well, that would be awesome.

Finally, I wonder if iterative "factorizations" are of interest? I.e. a struct that provides an implementation of ldiv! that under the hood uses one of the solvers from IterativeSolvers.jl. I started trying something out here, but I think it would possibly find a better home in IterativeSolvers.jl.

Ping @haampie

[alanderos91]

I think it would be nice if the various solvers had the same interface to create iterators (which would reduce the amount of boilerplate in e.g. https://github.com/haampie/JacobiDavidson.jl to support different solvers).

I've had to introduce some of that boilerplate in my projects a couple of times now, specifically to create allocation-free versions of CG, LSQR and LSMR. With a little extra effort, I think I could adapt what I have to implement iterators for those three methods. I'd like to contribute but don't want to duplicate work if other people already have (better) implementations.