The multinode Shepard operator is a linear combination of local polynomial interpolants with
inverse distance weighting basis functions. This operator can be rewritten as a blend of …

The problem of Lagrange interpolation of functions of two variables by quadratic
polynomials based on nodes which are vertices of a triangulation has been recently studied …

The triangular Shepard method, introduced by Little in 1983 [7], is a convex combination of
triangular basis functions with linear polynomials, based on the vertices of the triangles, that …

The triangular Shepard method is a fast and accurate scheme for interpolating scattered
data. In this paper, we introduce an improvement of the triangular Shepard method for …

In the interpolation method, in some cases, one often has a number of data points and its
derivatives, which are obtained by sampling or experimentation. In this case, the problem of …

As a natural extension of Birkhoff polynomial interpolation, Birkhoff rational interpolation is
difficult to be linearized. In this work, we strategically split the univariate Birkhoff rational …

In this article, families of non-linear subdivision schemes are presented that are based on
univariate polynomials up to degree three. These families of schemes are constructed by …

Abstract Abel-Whittaker series (1934) is viewed as a two-point Taylor series. It solves the
interpolation problem f (2 n)(1)= an, f (2 n+ 1)(0)= bn, n≥ 0, for an appropriate analytic …

In this paper, we introduce a novel two‐step modeling method to generalize cubic Hermite
interpolators on the space of probability measures P+(I) P _ &# x0002B;(I). First, we develop …

This paper discusses the use of local spline approximations to solve the Hermite-Birkhoff
problem. The solution to a specific problem using polynomial and non-polynomial local …