Geodesic
About the absolute value function with different nodes of Lagrange interpolation
Matematičeskie zametki SVFU, Tome 25 (2018) no. 2, pp. 48-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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Lagrange interpolation processes are considered for the following matrixes of interpolation nodes: the matrix of Chebyshev polynomial roots of the 1st kind, the matrix of Legendre polynomials roots, and the extended matrix of Legendre polynomials roots. For these matrixes the uniform convergence of Lagrange process of interpolation for the absolute value function proved. Also, we receive estimates on the order of convergence for each of these matrixes. To ensure the quality of convergence, the endpoints of the segment were added as nodes to the matrix of Legendre roots. However, for the absolute value function the order of convergence of the Legendre process does not change, but improves by approximately 8 times. For comparison, the negative result of equidistant nodes is taken.
Keywords: modulus of a number, Chebyshev and Legendre polynomials, extended matrix.
Mots-clés : interpolation, Lebesgue constant 
@article{SVFU_2018_25_2_a4,
     author = {V. B. Khokholov},
     title = {About the absolute value function with different nodes of {Lagrange} interpolation},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {48--54},
     year = {2018},
     volume = {25},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a4/}
}
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V. B. Khokholov. About the absolute value function with different nodes of Lagrange interpolation. Matematičeskie zametki SVFU, Tome 25 (2018) no. 2, pp. 48-54. http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a4/