相关论文: Rayleigh-Ritz variation method and connected-momen…
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge fixing method and which show an improved…
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and…
We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable…
We produce the first example of bounding total variation distance to stationarity and estimating mixing times via orthogonal polynomials diagonalization of discrete reversible Markov chains, the Karlin-McGregor approach.
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex…
We have developed a variational perturbation theory based on the Liouville-Neumann equation, which enables one to systematically compute the perturbative correction terms to the variationally determined wave functions of the time-dependent…
In this work we propose a generalization of the Moment Guided Monte Carlo method developed in [11]. This approach permits to reduce the variance of the particle methods through a matching with a set of suitable macroscopic moment equations.…
A variational approach is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing monomer-monomer force constants…
In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed difference method for solving two-dimensional Riesz space fractional advection-dispersion equation. The…
A new approach to deformation quantization on the cylinder considered as phase space is presented. The method is based on the standard Moyal formalism for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The results are…
We establish an equivalence between two classes of methods for solving fractional diffusion problems, namely, Reduced Basis Methods (RBM) and Rational Krylov Methods (RKM). In particular, we demonstrate that several recently proposed RBMs…
We generalize the worldline variational approach to field theory by introducing a trial action which allows for anisotropic terms to be induced by external 4-momenta of Green's functions. By solving the ensuing variational equations…
In this note we show that the standard \mbox{Rayleigh-Schr\"odinger} (RS) perturbation method gives the same result as the hypervirial pertubative method (HPM), for an approximate analytic expression for the energy eigenvalues of the…
We study a class of logarithmic Sobolev inequalities with a general form of the energy functional. The class generalizes various examples of modified logarithmic Sobolev inequalities considered previously in the literature. Refining a…
We study the modified Ricci solitons as a new class of Einstein type metrics that contains both Ricci solitons and $n$-quasi-Einstein metrics. This class is closely related to the construction of the Ricci solitons that are realised as…
Mixed orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss--Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the…
We investigate in this work the validity of linear stochastic models for nonlinear dynamical systems. We exploit as our basic tool a previously proposed Rayleigh-Ritz approximation for the effective action of nonlinear dynamical systems…