In the many particle physics the exact diagonalization (ED) is limited to small system sizes, like 4 x 4, on account of the restrictions of the computer memory. Whereas the stochastic diagonalization (SD) and the projector quantum Monte Carlo (PQMC) are not limited to a certain system size the limits in the parameter space of the analyzed physical model are at hoc not clear. For the two-dimensional tt'-Hubbard model we deduce the parameter space accessible to these two algorithms. Therefore we study several properties indicating the quality of the approximation of the ground stare received by SD or PQMC algorithm. Furthermore we present strategies to derive a possible failure of one of these two algorithms without the comparison with another algorithm by analyzing the numerical simulations in detail. Therefore we compare the both algorithms with the ED and mainly SD and PQMC among themselves. Additional we present some new results concerning the sign-problem and the appropriate choice of the test wave functions in the PQMC method. This leads to a new numerical algorithm combining SD and PQMC. (C) 2000 Elsevier Science B.V. All rights reserved.