Related papers: Rayleigh-Ritz variation method and connected-momen…
Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied…
Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…
The investigation of symmetry nonrestoration scenarios has led to a controversy, with certain nonperturbative approximation schemes giving indications in sharp disagreement with those found within conventional perturbation theory. A…
The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the…
We present results from numerical simulations of Rayleigh-Taylor turbulence, performed using a recently proposed lattice Boltzmann method able to describe consistently a thermal compressible flow subject to an external forcing. The method…
This study presents new closed-form estimators for the Dirichlet and the Multivariate Gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators…
In this paper, we introduce two types of variational integrators, one originating from the discrete Hamilton's principle while the other from Galerkin variational approach. It turns out that these variational integrators are equivalent to…
We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N=1 toy…
The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…
We consider random conformally invariant paths in the complex plane (SLEs). Using the Coulomb gas method in conformal field theory, we rederive the mixed multifractal exponents associated with both the harmonic measure and winding (rotation…
Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between…
We show that Prony's method provides the full solution to the nonlinear equations of the connected--moments expansion (CMX). Knowledge of all the parameters in the CMX ansatz is useful for the analysis of the convergence properties of the…
We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…
We propose a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems. The proposed method uses complex moments to extract the eigencomponents of interest from a…
We apply the connected moments expansion to simple quantum--mechanical examples and show that under some conditions the main equations of the approach are no longer valid. In particular we consider two--level systems, the harmonic…
We have previously shown (arXiv:1912.00033) that three approaches to relational quantum dynamics -- relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations -- are equivalent. Here we show that this `trinity'…
Given an approximate eigenvector, its (standard) Rayleigh quotient and harmonic Rayleigh quotient are two well-known approximations of the corresponding eigenvalue. We propose a new type of Rayleigh quotient, the homogeneous Rayleigh…
A novel class of conservative numerical methods for general conservative Stratonovich stochastic differential equations with multiple invariants is proposed and analyzed. These methods, which are called modified averaged vector field…
In Yang-Mills theories, variational calculations of the Rayleigh-Ritz type face the problem that on the one hand, calculability puts severe constraints on the space of test wave functionals; on the other hand, the test wave functionals have…
Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic…