相关论文: Multigrid Methods for the Computation of Propagato…
Complete spectra of the staggered Dirac operator $\Dirac$ are determined in quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An…
Recently, within the context of the phase space coherent state path integral quantisation of constrained systems, John Klauder introduced a reproducing kernel for gauge invariant physical states, which involves a projection operator onto…
Recently a new approach to analyze and create algebraic multigrid methods (AMG) for nonsymmetric and indefinite matrices was established. Convergence is measured in general norms induced by a certain HPD matrix $B$ and $B$-orthogonal…
Gauge theories can be described by assigning a vector space V(x) to each space time point x. A common set of complex numbers, C, is usually assumed to be the set of scalars for all the V{x}. This is expanded here to assign a separate set of…
In lattice field theory, field sparsening aims to replace quantum fields, or objects constructed from them, with approximations that preserve the appropriate symmetries and maintain many aspects of the physics that the fields determine. For…
In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods…
Kriging is a widely employed technique, in particular for computer experiments, in machine learning or in geostatistics. An important challenge for Kriging is the computational burden when the data set is large. This article focuses on a…
We construct the gauge field and graviton propagators in Euclidean AdS(d+1) space-time by two different methods. In the first method the gauge invariant Maxwell or linearized Ricci operator is applied directly to bitensor ansatze for the…
We present a new scheme for the general computation of cosmic propagators that allow to interpolate between standard perturbative results at low-k and their expected large-k resummed behavior. This scheme is applicable to any multi-point…
We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…
This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of "Algebraic Multi-Grid", but it…
This paper presents distributed conjugate gradient algorithms for distributed parameter estimation and spectrum estimation over wireless sensor networks. In particular, distributed conventional conjugate gradient (CCG) and modified…
In this paper, we investigate the use of multilevel Monte Carlo (MLMC) methods for estimating the expectation of discretized random fields. Specifically, we consider a setting in which the input and output vectors of numerical simulators…
The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the…
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven weights. Within…
Complete spectra of the staggered Dirac operator $\Dirac$ are determined in four-dimensional $SU(2)$ gauge fields with and without dynamical fermions. An attempt is made to relate the performance of multigrid and conjugate gradient…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…