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Lebesgue functions corresponding to a family of Lagrange interpolation polynomials

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Abstract

In this paper we obtain various explicit forms of the Lebesgue function corresponding to a family of Lagrange interpolation polynomials defined at an even number of nodes. We study these forms by using the derivatives up to the second order inclusive. We estimate exact values of Lebesgue constants for this family from below and above in terms of known parameters. In a particular case we obtain new convenient formulas for calculating these estimates.

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Authors and Affiliations

  1. Naberezhnye Chelny Institute of Social Pedagogical Technologies and Resources, 28 Nizametdinova str., Naberezhnye Chelny, 423806, Russia

    I. A. Shakirov

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  1. I. A. Shakirov
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Correspondence to I. A. Shakirov.

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Original Russian Text © I.A. Shakirov, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 7, pp. 77–89.

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Shakirov, I.A. Lebesgue functions corresponding to a family of Lagrange interpolation polynomials. Russ Math. 57, 66–76 (2013). https://doi.org/10.3103/S1066369X13070074

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  • DOI: https://doi.org/10.3103/S1066369X13070074

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