Unified Interface for Linear Solving

Actually, I think your approach is better: in most cases where you reuse a factorization, you would want to use the same tolerance.

The tolerance of the factorization could be thought of as a default tolerance, which could be overriden:

G = gmresfact(A,b; tolerance=eps())
G \ b # uses default tolerance
\(G,b; tolerance=1E-3)  # overrides default tolerance

but this may be overkill.