A new approach for constructing mock-Chebyshev grids

Ali Ibrahimoglu B. A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.44, sa.18, ss.14766-14775, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 18
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1002/mma.7741
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.14766-14775
  • Anahtar Kelimeler: mock-Chebyshev nodes, polynomial interpolation, Runge phenomenon, APPROXIMATION
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.