  We propose and study an improved method to calculate the fermionic
determinant of dynamical configurations. The evaluation or at least stochastic
estimation of ratios of fermionic determinants is essential for a recently
proposed updating method of smeared link dynamical fermions. This update
creates a sequence of configurations by changing a subset of the gauge links by
a pure gauge heat bath or over relaxation step. The acceptance of the proposed
configuration depends on the ratio of the fermionic determinants on the new and
original configurations. We study this ratio as the function of the number of
links that are changed in the heat bath update. We find that even when every
link of a given direction and parity of a 10fm^4 configuration is updated, the
average of the determinant ratio is still close to one and with the improved
stochastic estimator the proposed change is accepted with about 20%
probability. This improvement suggests that the new updating technique can be
efficient even on large lattices.
