We construct a locally-lexicographic SSOR preconditioner to accelerate the
parallel iterative solution of linear systems of equations for two improved
discretizations of lattice fermions: (i) the Sheikholeslami-Wohlert scheme
where a nonconstant block-diagonal term is added to the Wilson fermion mat
rix and (ii) renormalization group improved actions which incorporate coupl
ings beyond nearest neighbors of the lattice fermion fields. In case (i) we
find the block ll-SSOR-scheme to be more effective by a factor approximate
to 2 than odd-even preconditioned solvers in terms of convergence rates, a
t beta = 6.0. For type (ii) actions, we show that our preconditioner accele
rates the iterative solution of a linear system of hypercube fermions by a
factor of 3 to 4. (C) 1999 Elsevier Science B.V.