Related papers: Barycentric Interpolation Based on Equilibrium Pot…

This paper focuses on numerical approximation for fractional powers of elliptic operators on $2$-d manifolds. Firstly, parametric finite element method is employed to discretize the original problem. We then approximate fractional powers of…

This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…

We present the Polar framework for fully automating the analysis of classical and probabilistic loops using algebraic reasoning. The central theme in Polar comes with handling algebraic recurrences that precisely capture the loop semantics.…

This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE…

We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449--1466]. For a given semi-rational…

The computation of exact barycenters for a set of discrete measures is of interest in applications where sparse solutions are desired, and to assess the quality of solutions returned by approximate algorithms and heuristics. The task is…

In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great…

Developing reliable interatomic potential models with quantified predictive accuracy is crucial for atomistic simulations. Commonly used potentials, such as those constructed through the embedded atom method (EAM), are derived from…

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…

We examine the effect of numerical integration on the convergence of high order pyramidal finite element methods. Rational functions are indispensable to the construction of pyramidal interpolants so the conventional treatment of numerical…

We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…

We introduce the following linear combination interpolation problem (LCI): Given $N$ distinct numbers $w_1,\ldots w_N$ and $N+1$ complex numbers $a_1,\ldots, a_N$ and $c$, find all functions $f(z)$ analytic in a simply connected set…

Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…

With analytic applications in mind, in particular Beyond Endoscopy ([13]), we initiate the study of the elliptic part of the trace formula. Incorporating the approximate functional equation to the elliptic part we control the analytic…

We study cylindrically symmetric steady-state accretion of polytropic test matter spiraling onto the symmetry axis in power-law and logarithmic potentials. The model allows one to qualitatively understand the accretion process in a symmetry…

For the Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error constant under the maximum norm by using the finite element method (FEM). In solving the optimization…

The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…

Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…

Building upon Bennett's and Grosse-Erdmann's ideas falling under the conceptual umbrella of factorization of inequalities, we propose a unified approach towards the structure of certain Banach ideal spaces defined in terms of the least…

A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…