Related papers: A numerical treatment of Neuberger's lattice Dirac…
We discuss new approaches to the numerical implementation of Neuberger's operator for lattice fermions and the possible use of block spin transformations.
Recent developments have shown that a lot can be gained for QCD simulations from GPU hardware. This can be exploited especially in the case of Ginsparg-Wilson fermions when the com putational costs are particularly high. In this work, we…
I present several tricks to help implement the overlap Dirac operator numerically.
This introductory presentation describes the Overlap Dirac Operator, why it could be useful in numerical QCD, and how it can be implemented.
I derive the overlap Dirac operator starting from the overlap formalism, discuss the numerical hurdles in dealing with this operator and present ways to overcome them.
We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the…
In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite lattice spacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I…
I describe a Lanczos method to compute the Neuberger Operator and a multigrid algorithm for its inversion.
We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the…
We propose new techniques for the numerical implementation of the overlap-Dirac operator, which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger…
In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the…
The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of…
In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.
We present relaxation and preconditioning techniques which accelerate the inversion of the overlap operator by a factor of four on small lattices, with larger gains as the lattice size increases. These improvements can be used in both…
We review the exact results for microscopic Dirac operator spectra based on either Random Matrix Theory, or, equivalently, chiral Lagrangians. Implications for lattice calculations are discussed.
Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…
In this paper I propose the use of a lattice derivative operator that is equivalent to the ideal SLAC derivative operator in all lattice calculations, but without the prohibitively expensive computational cost of the latter. A pedagogical…