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On the uniform approximation of functions of bounded variation by Lagrange interpolation polynomials with a matrix \({\mathcal L}_n^{(\alpha_n,\beta_n)}\) of Jacobi nodes. (English. Russian original) Zbl 1466.41002

Izv. Math. 84, No. 6, 1224-1249 (2020); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 6, 197-222 (2020).
In this paper the author gives sufficient conditions that are more general than the conditions for the convergence of Lagrange interpolation polynomials with a matrix of interpolation nodes consisting of the zeros of Jacobi polynomials with particular parameters. They obtain sufficient conditions for the uniform convergence inside the interval \((0,\pi)\). This process is very interesting.

MSC:

41A05 Interpolation in approximation theory

Software:

MuST; Chebfun
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References:

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