Given is a system of linear equations $Ax=b$ and $A$ is of size n-by-n. If we use the generalized minimal residual method (GMRES) we iteratively calculate approximate solutions for Krylov subspaces of increasing dimension. Usually we abort prematurely, but eventually the Krylov subspace would be of the dimension $n$.
Doesn't that imply that GMRES is a direct solver instead of an iterative one since it should take at most $n$ steps to find a sufficient solution? Does it depend on the circumstances (e.g. the accuracy of the calculation)?