An extension of a mixed interpolation¿regression method using zeros of orthogonal polynomials Articles uri icon

publication date

  • November 2024

volume

  • 450

International Standard Serial Number (ISSN)

  • 0377-0427

Electronic International Standard Serial Number (EISSN)

  • 1879-1778

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.

keywords

  • equispaced nodes; interpolation¿regression operator; orthogonal polynomials; polynomial approximation