相关论文: The high-level error bound for shifted surface spl…
This article explores the influence of evenly spaced data points on radial-basis-function interpolation.
Recently, deep neural networks have been found to nearly interpolate training data but still generalize well in various applications. To help understand such a phenomenon, it has been of interest to analyze the ridge estimator and its…
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…
A thin plate spline surface for interpolation of smooth transfinite data prescribed along concentric circles was recently proposed by Bejancu, using Kounchev's polyspline method. The construction of the new `Beppo Levi polyspline' surface…
An explicit upper bound is derived for the modulus of divided difference for a smooth(not necessarily analytic) function defined on a smooth Jordan arc (or a smooth Jordan curve) in the complex plane. As an immediate application, an error…
We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating $n$ noisy training data points in…
Following their appearance in 2014, so-called shifted square and maximal functions have seen an eruption of use in the study of singular integral operators. In this paper, we will generalize a recent theorem of G. Dosidis, B. Park, and L.…
It's well known that in the high-level error bound for multiquadric interpolation there is a crucial constant lambda lying between 0 and 1 which connot be calculated or even approximated. The purpose of this paper is to answer this…
Based on the variable Hilbert scale interpolation inequality bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for the modulus of continuity of the inverse of bounded operators…
Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…
The research in the subfield of analytic number theory around error term of summation of sigma functions possesses a history which can be dated back to the mid-19th century when Dirichlet provided an $O(\sqrt{n})$ estimation of error term…
In this article we present a modification of classical Radial Basis Function (RBF) interpolation techniques aimed at reducing oscillations near discontinuities in one and two dimensions. Our approach introduces an adaptive mechanism by…
Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing…
We consider the Schr\"odinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in…
This paper deals with the error estimate in problems of periodic homogenization. The methods used are those of the periodic unfolding. We give the upper bound of the distance between the unfolded gradient of a function belonging to…
Convergence rates for $L_2$ approximation in a Hilbert space $H$ are a central theme in numerical analysis. The present work is inspired by Schaback (Math. Comp., 1999), who showed, in the context of best pointwise approximation for radial…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
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…
This note is the updated outline of the article "Interpolational properties of planar spiral curves", Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The main result establishes boundary regions for spiral and…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…