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