In this work we propose a new method for univariate polynomial interpolation based on what
we call mapped bases. As theoretically shown, constructing the interpolating function via the …

This paper examines the problem of extrapolation of an analytic function for x> 1 given N+ 1
perturbed samples from an equally spaced grid on [-1, 1]. For a function f on [-1, 1] that is …

The main goal of the present paper is to extend the interpolation via the so-called mapped
bases without resampling to any basis and dimension. So far indeed, we investigated the …

We consider the problem of approximating a smooth function from finitely many pointwise
samples using ℓ^ 1 ℓ 1 minimization techniques. In the first part of this paper, we introduce …

This work is concerned with the interpolation of a function f when using a low number of
interpolation points, as required by the finite element method for solving PDEs numerically …

Motivated by polynomial approximations of differential forms, we study analytical and
numerical properties of a polynomial interpolation problem that relies on function averages …

The mapped bases or Fake Nodes Approach (FNA), introduced in De Marchi et al.(J Comput
Appl Math 364: 112347, 2020c), allows to change the set of nodes without the need of …

We consider the problem of approximating an analytic function on a compact interval from its
values at distinct points. When the points are equispaced, a recent result (the so-called …

In this paper, we introduce the class of (β, γ)-Chebyshev functions and corresponding points,
which can be seen as a family of generalized Chebyshev polynomials and points. For the (β …

We consider approximating analytic functions on the interval [-1, 1] from their values at a set
of m+ 1 equispaced nodes. A result of Platte, Trefethen & Kuijlaars states that fast and stable …