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Lagrange interpolation at real projections of Leja sequences for the unit disk


Authors: Jean-Paul Calvi and Phung Van Manh
Journal: Proc. Amer. Math. Soc. 140 (2012), 4271-4284
MSC (2010): Primary 41A05, 41A63
DOI: https://doi.org/10.1090/S0002-9939-2012-11291-2
Published electronically: April 23, 2012
MathSciNet review: 2957218
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Abstract: We show that the Lebesgue constants of the real projection of Leja sequences for the unit disk grow like a polynomial. The main application is the first construction of explicit multivariate interpolation points in $ [-1,1]^N$ whose Lebesgue constants also grow like a polynomial.


References [Enhancements On Off] (What's this?)

  • 1. L. Białas-Cież and J.-P. Calvi.
    Pseudo Leja sequences.
    Ann. Mat. Pura e Appl., 191:53-75, 2012.
  • 2. L. Brutman.
    Lebesgue functions for polynomial interpolation--a survey.
    Ann. Numer. Math., 4(1-4):111-127, 1997.
    The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin. MR 1422674 (97m:41003)
  • 3. J.-P. Calvi.
    Intertwining unisolvent arrays for multivariate Lagrange interpolation.
    Adv. Comput. Math., 23(4):393-414, 2005. MR 2137463 (2006a:41002)
  • 4. J.-P. Calvi and Phung Van Manh.
    On the Lebesgue constant of Leja sequences for the unit disk and its applications to multivariate interpolation.
    J. Approx. Theory, 163(5):608-622, 2011. MR 2784514
  • 5. H. Ehlich and K. Zeller.
    Auswertung der Normen von Interpolationsoperatoren.
    Math. Ann., 164:105-112, 1966. MR 0194799 (33:3005)
  • 6. A. P. Goncharov.
    On growth of norms of Newton interpolating operators.
    Acta Math. Hungar., 125(4):299-326, 2009. MR 2564431 (2011a:41030)
  • 7. T. H. Gronwall.
    A sequence of polynomials connected with the $ n$th roots of unity.
    Bull. Amer. Math. Soc., 27:275-279, 1921. MR 1560416
  • 8. T. J. Rivlin.
    An introduction to the approximation of functions.
    Dover Publications Inc., New York, 1981.
    Corrected reprint of the 1969 original, Dover Books on Advanced Mathematics. MR 634509 (83b:41001)
  • 9. R. Taylor and V. Totik.
    Lebesgue constants for Leja points.
    IMA J. Numer. Anal., 30:462-486, 2010. MR 2608468 (2011d:41003)

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Additional Information

Jean-Paul Calvi
Affiliation: Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France
Email: jean-paul.calvi@math.univ-toulouse.fr

Phung Van Manh
Affiliation: Institut de Mathématiques, Université de Toulouse III and CNRS (UMR 5219), 31062, Toulouse Cedex 9, France – and – Department of Mathematics, Hanoi University of Education, 136 Xuan Thuy street, Caugiay, Hanoi, Vietnam
Email: manhlth@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2012-11291-2
Keywords: Lagrange interpolation, Lebesgue constants, Leja sequences
Received by editor(s): February 21, 2011
Received by editor(s) in revised form: June 3, 2011
Published electronically: April 23, 2012
Communicated by: Walter Van Assche
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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