Related papers: Sinc approximation of algebraically decaying funct…
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. However, linear extrapolation is used far more often in…
The main result in this paper is an error estimate for interpolation biharmonic polysplines in an annulus $A\left( r_{1},r_{N}\right) $, with respect to a partition by concentric annular domains $A\left( r_{1} ,r_{2}\right) ,$ ....,…
An extension of the Ising spin configurations to continuous functions is used for an exact representation of the Random Field Ising Model's order parameter in terms of disagreement percolation. This facilitates an extension of the recent…
The purpose of this article is to provide new error estimates for a popular type of SBF approximation on the sphere: approximating by linear combinations of Green's functions of polyharmonic differential operators. We show that the $L_p$…
We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…
Given a nondecreasing function $f$ on $[-1,1]$, we investigate how well it can be approximated by nondecreasing algebraic polynomials that interpolate it at $\pm 1$. We establish pointwise estimates of the approximation error by such…
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…
For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
We introduce a technique to estimate a linear operator by embedding it in a family $A_t$ of operators, $t\in(\sigma_0,\infty)$, with suitable curvature properties. One can then estimate the norm of each $A_t$ by bounds that hold in the…
The functional interpolation problem on a continual set of nodes by an integral continued C-fraction is studied. The necessary and sufficient conditions for its solvability are found. As a particular case, the considered integral continued…
Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite…
Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the…
A formal sum $\sum_n f(S_n)$ may be seen as the integral $\int f dN$ with respect to random point process $N(A)=|\{n:S_n\in A\}|$. We study its convergence beyond the well known context of Lebesgue integrable functions, admitting…
Ordinal regression is a classification task where classes have an order and prediction error increases the further the predicted class is from the true class. The standard approach for modeling ordinal data involves fitting parallel…
This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a better convergence rate in more general cases, and 2) explicit…
We prove a decay estimate for an operator that arises in two-dimensional scattering problem.
In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…