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On growth of norms of Newton interpolating operators

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Abstract

We consider the problem of growth of the sequence of Lebesgue constants corresponding to the Newton interpolation and estimate the growth of this sequence in the case of a nested family of Chebyshev’s points.

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References

  1. L. Brutman, Lebesgue functions for polynomial interpolation — a survey, Ann. Numer. Math., 4 (1997), 111–127.

    MATH  MathSciNet  Google Scholar 

  2. A. Goncharov, What is the size of the Lebesgue constant for Newton interpolation?, in: Constructive Theory of Functions (Varna, 2005), edited by B. D. Bojanov, p. 144.

  3. E. Levin and B. Shekhtman, Two problems on interpolation, Constr. Approx., 11 (1995), 513–515.

    Article  MATH  MathSciNet  Google Scholar 

  4. Paul G. Nevai, Orthogonal Polynomials, Memoirs of AMS, Vol.18, 123 (Providence, 1979).

  5. T. J. Rivlin, The Chebyshev Polynomials, second edition, Pure and Applied Mathematics (New York, 1990).

    Google Scholar 

  6. E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Springer-Verlag (1997).

  7. G. Szegö, Orthogonal Polynomials, fourth edition, AMS Coll. Publ., Vol. 23 (Providence, 1975).

  8. R. Taylor and V. Totik, Lebesgue constants for Leja points, IMA Journal of Num. Anal. (to appear).

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Correspondence to A. P. Goncharov.

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Goncharov, A.P. On growth of norms of Newton interpolating operators. Acta Math Hung 125, 299–326 (2009). https://doi.org/10.1007/s10474-009-9023-z

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  • DOI: https://doi.org/10.1007/s10474-009-9023-z

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