Related papers: A Bernstein Polynomial Collocation Method for the …

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…

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 use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation…

We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced…

We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding,…

In this paper, we extend the Generalized Finite Difference Method (GFDM) on unknown compact submanifolds of the Euclidean domain, identified by randomly sampled data that (almost surely) lie on the interior of the manifolds. Theoretically,…

We use novel integral representations developed by the second author to prove certain rigorous results concerning elliptic boundary value problems in convex polygons. Central to this approach is the so-called global relation, which is a…

We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…

We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…

We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving…

We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…

We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…

In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results…

We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…

Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…

In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study…

We explain how to use smooth bivariate splines of arbitrary degree to solve the exterior Helmholtz equation based on a Perfectly Matched Layer (PML) technique. In a previous study (cf. [26]), it was shown that bivariate spline functions of…

In the theory of second-order, nonlinear elliptic and parabolic equations, obtaining local or global gradient bounds is often a key step for proving the existence of solutions but it may be even more useful in many applications, for example…

The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be solved in the least squares sense is then a rectangular…