Two new algorithms of particular interest in unquenched latticequantum chromodynamic simulations (lattice QCD) are studied: theall-point quark propagator algorithm for extracting full quarkpropagators, and the combined truncated determinant/multibosonalgorithm for simulating full dynamical QCD. In each case, a detailed study of the statistical properties andefficiency of the algorithm is made, allowing optimization ofthe relevant parameters, as well as an application of the algorithmto a problem of physical interest in lattice QCD. In the firstcase, the all-point method is applied to the problem of extractingparameters of the QCD chiral Lagrangian from lattice QCD measurementsof hadronic correlators. In the second case, the truncated determinant/multiboson method is used to search for a potential Sharpe-Singletonchiral phase in the strong-coupling region of unquenched QCD
