Related papers: Interpolation Error Estimates for Harmonic Coordin…
We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three dimensional maximum…
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time…
The notion of interpolation and extrapolation is fundamental in various fields from deep learning to function approximation. Interpolation occurs for a sample $x$ whenever this sample falls inside or on the boundary of the given dataset's…
The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from…
We here specialize the standard matrix-valued polynomial interpolation to the case where on the imaginary axis the interpolating polynomials admit various symmetries: Positive semidefinite, Skew-Hermitian, $J$-Hermitian, Hamiltonian and…
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 develop interpolation error estimates for general order standard and serendipity edge and face virtual elements in two and three dimensions. Contextually, we investigate the stability properties of the associated L2 discrete bilinear…
Time delay estimation has long been an active area of research. In this work, we show that compressive sensing with interpolation may be used to achieve good estimation precision while lowering the sampling frequency. We propose an…
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…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…
The aim of this paper is to show that, for any $p \in [1,\infty)$, the $W^{1,p}$-anisotropic interpolation error estimate holds on quadrilateral isoparametric elements verifying the maximum angle condition ($MAC$) and the property of…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate…
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…
Some basic mathematical tools such as convex sets, polytopes and combinatorial topology, are used quite heavily in applied fields such as geometric modeling, meshing, computer vision, medical imaging and robotics. This report may be viewed…
Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is…
Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…