A new approach for constructing mock-Chebyshev grids


Ali Ibrahimoglu B. A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.44, no.18, pp.14766-14775, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 18
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.7741
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Page Numbers: pp.14766-14775
  • Keywords: mock-Chebyshev nodes, polynomial interpolation, Runge phenomenon, APPROXIMATION

Abstract

Polynomial interpolation with equidistant nodes is notoriously unreliable due to the Runge phenomenon and is also numerically ill-conditioned. By taking advantage of the optimality of the interpolation processes on Chebyshev nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev points, which are selected from a satisfactory uniform grid, for polynomial interpolation. Yet little literature exists on the computation of these points. In this study, we investigate the properties of the mock-Chebyshev nodes and propose a subsetting method for constructing mock-Chebyshev grids. Moreover, we provide a precise formula for the cardinality of a satisfactory uniform grid. Some numerical experiments using the points obtained by the method are given to show the effectiveness of the proposed method, and numerical results are also provided.