  We show that the standard Lanczos algorithm can be efficiently implemented
statistically and self consistently improved, using the stochastic reconfigurat
ion method, which has been recently introduced to stabilize the Monte Carlo
sign problem instability. With this scheme a few Lanczos steps over a given
variational wavefunction are possible even for large size as a particular case
of a more general and more accurate technique that allows to obtain lower
variational energies. This method has been tested extensively for a strongly
correlated model like the t-J model. With the standard Lanczos technique it is
possible to compute any kind of correlation functions, with no particular
computational effort. By using that the variance $<H^2>-<H>^2$ is zero for an
exact eigenstate, we show that the approach to the exact solution with few
Lanczos ite rations is indeed possible even for $\sim 100$ electrons for
reasonably good initial wavefunctions.The variational stochastic
reconfiguration technique presented here allows in general a many-parameter
energy optimization of any computable many-body wavefunction, including for
inst ance generic long range Jastrow factors and arbitrary site dependent
orbital determinants. This scheme improves further the accuracy of the
calculation, especially for long distance correlation functions.
