Preconditioning of improved and "perfect" fermion actions

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 matrix and (ii) renormalization group improved actions which incorporate couplings 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, at beta = 6.0. For type (ii) actions, we show that our preconditioner accelerates the iterative solution of a linear system of hypercube fermions by a factor of 3 to 4. (C) 1999 Elsevier Science B.V.