  In this paper we compare numerical results for the ground state of the
Hubbard model obtained by Quantum-Monte-Carlo simulations with results from
exact and stochastic diagonalizations. We find good agreement for the ground
state energy and superconducting correlations for both, the repulsive and
attractive Hubbard model. Special emphasis lies on the superconducting
correlations in the repulsive Hubbard model, where the small magnitude of the
values obtained by Monte-Carlo simulations gives rise to the question, whether
these results might be caused by fluctuations or systematic errors of the
method. Although we notice that the Quantum-Monte-Carlo method has convergence
problems for large interactions, coinciding with a minus sign problem, we
confirm the results of the diagonalization techniques for small and moderate
interaction strengths. Additionally we investigate the numerical stability and
the convergence of the Quantum-Monte-Carlo method in the attractive case, to
study the influence of the minus sign problem on convergence. Also here in the
absence of a minus sign problem we encounter convergence problems for strong
interactions.

Condensed Matter