The PZ method for estimating determinant ratios, with applications

The current work was motivated by our search for an alternative implementation of the Hybrid Monte Carlo (HCM) algorithm in lattice QCD which does not require the use of pseudofermions Our proposed algorithm requires the estimation of determinant ratios det M1/det M2 where the matrices M1 and M2 satisfy the following conditions: M1 and M2 are huge (N x N), where N∝1060; the eigenvalues of M1 and M2 have positive real parts; det Mi are O(N), but det M1/det M2 is O(1); and the eigenvalues of M2 are continuous perturbations of the eigenvalues of M1. In this paper we present a new method for estimating such determinant ratios, which takes advantage of Pade approximation of Z2 noise vectors (hence the acronym 'PZ'). The potential application of related methods to estimating the density of states is also indicated