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

Elías Berriochoa, Alicia Cachafeiro, Héctor García-Rábade and José Manuel García-Amor
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Elías Berriochoa: Departamento de Matemática Aplicada I, Universidad de Vigo, 36310 Vigo, Spain
Alicia Cachafeiro: Departamento de Matemática Aplicada I, Universidad de Vigo, 36310 Vigo, Spain
Héctor García-Rábade: Departamento de Matemática Aplicada II, Universidad de Vigo, 32004 Ourense, Spain
José Manuel García-Amor: Xunta de Galicia, Instituto E. S. Valle Inclán, 36001 Pontevedra, Spain

Mathematics, 2022, vol. 10, issue 15, 1-14

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.

Keywords: Lagrange interpolation; Chebyshev nodal systems; Chebyshev–Lobatto nodal systems; absolute value approximation; rate of convergence; Gibbs–Wilbraham phenomena (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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