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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)
To be kept in solitude is to be kept in pain, and put on the road to madness. The United States engages in extreme practices of solitary confinement that maximize isolation and sensory deprivation of prisoners. The length is often indefinite and can stretch for weeks, months, years, or decades. Under these conditions, both healthy prisoners and those with(More)
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 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.