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A Note on Lagrange Interpolation of | x | on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases

Author

Listed:
  • Elías Berriochoa

    (Departamento de Matemática Aplicada I, Universidad de Vigo, 36310 Vigo, Spain
    These authors contributed equally to this work.)

  • Alicia Cachafeiro

    (Departamento de Matemática Aplicada I, Universidad de Vigo, 36310 Vigo, Spain
    These authors contributed equally to this work.)

  • Héctor García-Rábade

    (Departamento de Matemática Aplicada II, Universidad de Vigo, 32004 Ourense, Spain
    These authors contributed equally to this work.)

  • José Manuel García-Amor

    (Xunta de Galicia, Instituto E. S. Valle Inclán, 36001 Pontevedra, Spain
    These authors contributed equally to this work.)

Abstract

Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the function | x | on [ − 1 , 1 ] , using Chebyshev and Chebyshev–Lobatto nodal systems with an even number of points. Moreover, with respect to the odd cases, relevant changes in the shape and the extrema of the error are given.

Suggested Citation

  • Elías Berriochoa & Alicia Cachafeiro & Héctor García-Rábade & José Manuel García-Amor, 2022. "A Note on Lagrange Interpolation of | x | on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases," Mathematics, MDPI, vol. 10(15), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2558-:d:869270
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    References listed on IDEAS

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    1. Berriochoa, E. & Cachafeiro, A. & Díaz, J., 2015. "Gibbs phenomenon in the Hermite interpolation on the circle," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 274-286.
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