  We show that, in four dimensions, the quark propagator is affected by
round-off errors for large values of the quark mass am and the time extent T/a
even when double precision arithmetics is used to compute it. We introduce a
definition of the solver residual which is sensitive to the problem and apply a
Schwarz alternating procedure to compute the propagator in a number of
sub-domains in the time direction. The effectiveness of the method is
demonstrated in a numerical computation of the free one-dimensional Dirac
propagator.
