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 …

In this work, we extend the so-called mapped bases or fake nodes approach to the
barycentric rational interpolation of Floater–Hormann and to AAA approximants. More …

Based on Cauchy's integral formula and conformal maps, this paper presents a new method
for constructing barycentric rational interpolation formulae for complex functions, which may …

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 …

In this paper, we collect the basic theory and the most important applications of a novel
technique that has shown to be suitable for scattered data interpolation, quadrature, bio …

In this paper, we present recent solutions to the problem of approximating functions by
polynomials for reducing in a substantial manner two well-known phenomena: Runge and …

We investigate the use of the so-called mapped bases or fake nodes approach in the
framework of numerical integration. We show that such approach is able to mitigate the …

In a hand–eye collaborative measurement system, the measurement error caused by the
position change of an industrial robot end can create challenges during the high-precision …

Abstract Gauss–Legendre quadrature, Clenshaw–Curtis quadrature and the trapezoid rule
are powerful tools for numerical integration of analytic functions. For nearly singular …

A well-known result in linear approximation theory states that the norm of the operator,
known as the Lebesgue constant, of polynomial interpolation on an interval grows only …