Luscher's local bosonic algorithm for Monte Carlo simulations of quant
um field theories with fermions is applied to the simulation of a poss
ibly supersymmetric Yang-Mills theory with a Majorana fermion in the a
djoint representation. Combined with a correction step in a two-step p
olynomial approximation scheme, the obtained algorithm seems to be pro
mising and could be competitive with more conventional algorithms base
d on discretized classical (''molecular dynamics'') equations of motio
n. The application of the considered polynomial approximation scheme t
o optimized hopping parameter expansions is also discussed.