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Polynomial approximations to the inverse of the fermion matrix are used tofilter the dynamics of the upper energy scales in HMC simulations. The use of amultiple time-scale integration scheme allows the filtered pseudofermions to beevolved using a coarse step size. We introduce a novel generalisation of thenested leapfrog which allows for far greater flexibility in the choice of timescales. We observe a reduction in the computational expense of the moleculardynamics integration of between 3--5 which improves as the quark massdecreases.

Polynomial Filtered HMC -- an algorithm for lattice QCD with dynamical quarks