Related papers: An iterative Monte Carlo method to solve nonlinear…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…
We present a method of solving a nonlinear Dirichlet problem with discontinuous boundary data and we give a probabilistic representation of the solution using the nonlocal branching process associated with the nonlinear term of the…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated…
Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…
We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.
Using non-linear difference equations, combined with symbolic computations, we make a detailed study of the running times of numerous variants of the celebrated Quicksort algorithms, where we consider the variants of single-pivot and…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
We present a numerical method and computer code to calculate the radiative transfer and excitation of molecular lines. Formulating the Monte Carlo method from the viewpoint of cells rather than photons allows us to separate local and…
An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the…
This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…
In Monte Carlo integration an accurate and reliable determination of the numerical intregration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In…