An extension of a mixed interpolation–regression method using zeros of orthogonal polynomials
Francesco Dell’Accio, Francisco Marcellán, Federico Nudo
Abstract
The constrained mock-Chebyshev least squares approximation (CMCLS-approximation) is a method that has been recently introduced. It operates on a grid of equidistant points, aiming to eliminate the Runge phenomenon. The implementation of the idea behind this approximation method involves interpolating the function exclusively on the subset of nodes closer to the set of Chebyshev–Lobatto nodes of a suitable order and using the remaining nodes to enhance the accuracy of the approximation through a simultaneous regression. The main goal of this article is to extend the CMCLS-approximation through the interpolation on zeros of orthogonal polynomials, leveraging their inherent favorable properties.