  For some models of interacting fermions the known solution to the notorious
sign-problem in Monte Carlo (MC) simulations is to work with macroscopic
fermionic determinants; the price, however, is a macroscopic scaling of the
numerical effort spent on elementary local updates. We find that the {\it
ratio} of two macroscopic determinants can be found with any desired accuracy
by considering truncated (local in space and time) matices. In this respect, MC
for interacting fermionic systems becomes similar to that for the
sign-problem-free bosonic systems with system-size independent update cost. We
demonstrate the utility of the truncated-determinant method by simulating the
attractive Hubbard model within the MC scheme based on partially summed Feynman
diagrams. We conjecture that similar approach may be useful in other
implementations of the sign-free determinant schemes.
