Related papers: Weighted Lagrange Interpolation Using Orthogonal P…
We present a method to obtain weight functions associated with linear and quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional of the orthogonal polynomial sequences in the Askey scheme,…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
We use $L^2$ estimates for the $\bar\partial$ equation to find geometric conditions on discrete interpolating varieties for weighted spaces $A_p(\C)$ of entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$. In particular, we…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…
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 investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
New sequences of orthogonal polynomials with respect to the weight functions $e^{-x} \rho_\nu(x),\ e^{- 1/x} x^{-1} \rho_{\nu} (x), \rho_{\nu}(x)= 2 x^{\nu/2} K_\nu(2\sqrt x),\ x >0, \nu \in \mathbb{R}$, where $K_\nu(z)$ is the modified…
The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…
We give sufficient conditions for the bounded law of the iterated logarithms for strictly stationary random fields when the summation is done on rectangle. The study is done by the control of an appropriated maximal function. The case of…
We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore…
The paper deals with the approximate solution of integro-differential equations of Prandtl's type. Quadrature methods involving ``optimal'' Lagrange interpolation processes are proposed and conditions under which they are stable and…
Let X be a Banach space and $1\le p<\infty$. We prove interpolation inequalities of Marcinkiewicz-Zygmund type for X-valued polynomials g of degree $\le n$ on $R$, \[c_p (\sum\limits_{i=1}^{n+1} \mu_i \| g(t_i)e^{-t_i^2 /2} \|^p)^{1/p} \le…
The conjecture by Steklov was solved negatively by Rakhmanov in 1979. His original proof was based on the formula for orthogonal polynomial obtained by adding point masses to the measure of orthogonality. In this note, we show how this…
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method…
This paper deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate…
We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials.…
It is shown that the orthogonal polynomials, corresponding to the oscillatory weight $e^{\im\omega x}$, exists if $\omega$ is a transcendental number and $\tan\omega/\omega\in\Q$. Also, it is proved that such orthogonal polynomials exist…