Related papers: Remarkable upper bounds for the interpolation erro…
Traditional CNC technology mostly uses the method of increasing the degree of interpolation polynomial when constructing $C^2$ continuous NURBS curves, but this often leads to the appearance of Runge phenomenon in interpolation curves.…
A new error bound which is better than the current exponential-type error bound is presented in this paper.
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…
Asymmetry measurements are common in collider experiments and can sensitively probe particle properties. Typically, data can only be measured in a finite region covered by the detector, so an extrapolation from the visible asymmetry to the…
We prove tight bounds on the site percolation threshold for $k$-uniform hypergraphs of maximum degree $\Delta$ and for $k$-uniform hypergraphs of maximum degree $\Delta$ in which any pair of edges overlaps in at most $r$ vertices. The…
Radial basis functions (RBFs) play an important role in function interpolation, in particular in an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a parameter called the shape parameter. There are many…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to $H^1_0(\Omega)$. We establish in this case some error bounds for…
Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the…
We consider shells of non-constant thickness in three dimensional Euclidean space around surfaces which have bounded principal curvatures. We derive Korn's interpolation (or the so called first and a half (The inequality first introduced in…
We consider Lagrange interpolation on the set of finitely many intervals. This problem is closely related to the least deviating polynomial from zero on such sets. We will obtain lower and upper estimates for the corresponding Lebesgue…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
We prove explicit doubling inequalities and obtain uniform upper bounds (under $(d-1)$-dimensional Hausdorff measure) of nodal sets of weak solutions for a family of linear elliptic equations with rapidly oscillating periodic coefficients.…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
We compute the non--trivial infrared $\phi^4_3$--fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum space renormalization group. We choose a coordinate…
In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…
The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…
The study of interpolation nodes and their associated Lebesgue constants are central to numerical analysis, impacting the stability and accuracy of polynomial approximations. In this paper, we will explore the Morrow-Patterson points, a set…