We study analytically the computational cost of the Generalised Hybrid Monte Carlo (GHMC) algorithm for free field theory. We calculate the Metropolis acceptance probability for leapfrog and higher-order discretisations of the Molecular Dynamics (MD) equations of motion. We show how to calculate autocorrelation functions of arbitrary polynomial operators,… (More)
We present first results from a simulation of quenched overlap fermions with improved gauge field action. Among the quantities we study are the spectral properties of the overlap operator, the chiral condensate and topological charge, quark and hadron masses, and selected nucleon matrix elements. To make contact with continuum physics, we compute the… (More)
We describe an implementation of the Rational Hybrid Monte Carlo (RHMC) algorithm for dynamical computations with two flavours of staggered quarks. We discuss several variants of the method, the performance and possible sources of error for each of them, and we compare the performance and results to the inexact R algorithm.
We review the theory of elliptic functions leading to Zolotarev's formula for the sign function over the range ε ≤ |x| ≤ 1. We show how Gauß' arithmetico-geometric mean allows us to evaluate elliptic functions cheaply, and thus to compute Zolotarev coefficients " on the fly " as a function of ε. This in turn allows us to calculate the matrix functions sgn… (More)
We consider the Rational Hybrid Monte Carlo algorithm for performing exact 2+1 flavour fermion simulations. The specific cases of asqtad and domain wall fermions are considered. We find that in both cases the na¨ıve performance is similar to conventional hybrid algorithms.
We discuss the work of the QCDSP collaboration to build an inexpensive Teraflop scale massively parallel computer suitable for computations in Quantum Chromodynamics (QCD). The computer is a collection of nodes connected in a four dimensional toroidial grid with nearest neighbor bit serial communications. A node is composed of a Texas Instruments Digital… (More)
This is the write-up of three lectures on algorithms for dynamical fermions that were given at the ILFTN workshop 'Perspectives in Lattice QCD' in Nara during November 2005. The first lecture is on the fundamentals of Markov Chain Monte Carlo methods and introduces the Hybrid Monte Carlo (HMC) algorithm and symplectic integrators; the second lecture covers… (More)
We review the theory of optimal polynomial and rational Chebyshev approximations, and Zolotarev's formula for the sign function over the range ǫ ≤ |z| ≤ 1. We explain how rational approximations can be applied to large sparse matrices efficiently by making use of partial fraction expansions and multi-shift Krylov space solvers.