Related papers: On the filtered polynomial interpolation at Chebys…
In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
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…
Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization of the polynomial interpolation theory developed for a node…
The maximum volume principle is investigated as a means to solve the following problem: Given a set of arbitrary interpolation nodes, how to choose a set of polynomial basis functions for which the Lagrange interpolation problem is…
For Lagrange polynomial interpolation on open arcs $X=\gamma$ in $\mathbb{C}$, it is well-known that the Lebesgue constant for the family of Chebyshev points ${\bf{x}}_n:=\{x_{n,j}\}^{n}_{j=0}$ on $[-1,1]\subset \mathbb{R}$ has growth order…
We obtain new effective results in best approximation theory, specifically moduli of uniqueness and constants of strong unicity, for the problem of best uniform approximation with bounded coefficients, as first considered by Roulier and…
The challenge to measure exposures regularly forces financial institutions into a choice between an overwhelming computational burden or oversimplification of risk. To resolve this unsettling dilemma, we systematically investigate replacing…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…
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…
The goal of this article is to provide a general multivariate framework that synthesizes well-known non-tensorial polnomial interpolation schemes on the Padua points, the Morrow-Patterson-Xu points and the Lissajous node points into a…
Higher-degree polynomial interpolations carried out on uniformly distributed nodes are often plagued by {\it overfitting}, known as Runge's phenomenon. This work investigates Runge's phenomenon and its suppression in various versions of the…
Starting from de la Vall\'ee Poussin type (VP) interpolation, the authors have recently introduced a family of interpolating polynomial scaling and wavelet bases generating the approximation and detail spaces of a non-standard…
In this paper we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional first and second kind Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality…
In this paper, we study the optimal general convergence rates for quadratures derived from Chebyshev points. By building on the aliasing errors on integration of Chebyshev polynomials, together with the asymptotic formulae on the…
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs).…
We propose a spectral method based on the implementation of Chebyshev polynomials to study a model of conservation laws on network. We avoid the Gibbs phenomenon near shock discontinuities by implementing a filter in the frequency space in…
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runtime and linear storage cost. The generalisation supports any…
In this paper, we focus on barycentric weights and Lebesgue constants for Lagrange interpolation of arbitrary node distributions on \([-1,1]\). The following three main works are included: estimates of upper and lower bounds on the…