Abstract

This work examines several methods of computing all-to-all quark propagators for use in Lattice QCD spectrum calculations. The first of these methods employs the introduction of stochastic sources across the entire lattice, which are then 'diluted' to create an improved estimator of the all-to-all quark propagator. It is concluded that a moderate level of 'dilution' preconditioning is optimal. Secondly, an exact algorithm for computing smeared all-to-all propagators is introduced and tested. While this algorithm works well on small lattices, the computational cost scales like the square of the spatial volume and is thus impractical for larger volumes. Finally, a new way of stochastically estimating smeared all-to-all propagators is introduced. For an equal cost, this method exhibits a drastic decrease in error compared to conventional stochastic estimation. New dilution schemes are also introduced. Both the exact and new stochastic methods are then applied to a calculation of the low-lying excited nucleon spectrum on N_f = 2 + 1 dynamical lattices.