Related papers: Speed and Adaptability of Overlap Fermion Algorith…
We present promising initial results of our adaptive multigrid solver developed for application directly to the non-Hermitian Wilson-Dirac system in 4 dimensions, as opposed to the solver developed in [1] for the corresponding normal…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
This remark describes efficiency improvements to Algorithm 916 [Zaghloul and Ali 2011]. It is shown that the execution time required by the algorithm, when run at its highest accuracy, may be improved by more than a factor of two. A better…
We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton…
Computing quark propagators with overlap fermions requires the solution of a shifted unitary linear system. Jagels and Reichel have shown that for such systems it is possible to construct a minimal residual algorithm by short recurrences.…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
The overlap Dirac operator in lattice QCD requires the computation of the sign function of a matrix. While this matrix is usually Hermitian, it becomes non-Hermitian in the presence of a quark chemical potential. We show how the action of…
We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than $2$. Specifically, we obtain a…
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…
We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix…
In this paper we describe a new algorithm called Fast Adaptive Sequencing Technique (FAST) for maximizing a monotone submodular function under a cardinality constraint $k$ whose approximation ratio is arbitrarily close to $1-1/e$, is…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…
Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both…
We test exact and approximate Ginsparg-Wilson fermions with respect to their chiral and scaling behavior in the 2-flavor Schwinger model. We first consider explicit approximate GW fermions in a short range, then we proceed to their chiral…
When minimizing the sum of a convex and a strongly convex function, or when finding the zero of the sum of a monotone operator and a strongly monotone operator, Chambolle and Pock (2010) and Davis and Yin (2015) proposed accelerated…
We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap fermions. We derive a method which can be used to account for the delta function in the fermionic force caused by the differential of the sign function. We discuss the…
A modern Fortran implementation of three Dirac operators (Wilson, Brillouin, Susskind) in lattice QCD is presented, based on OpenMP shared-memory parallelization and SIMD pragmas. The main idea is to apply a Dirac operator to $N_v$ vectors…
We show how rational function approximations to the logarithm, such as $\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$, can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…