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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Stieltjes polynomials and Lagrange interpolation
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by Sven Ehrich and Giuseppe Mastroianni PDF
Math. Comp. 66 (1997), 311-331 Request permission

Abstract:

Bounds are proved for the Stieltjes polynomial $E_{n+1}$, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials $P_n$. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials $G_n$. Applying these results, convergence theorems are proved for the Lagrange interpolation process with respect to the zeros of $E_{n+1}$, and for the extended Lagrange interpolation process with respect to the zeros of $P_n E_{n+1}$ in the uniform and weighted $L^p$ norms. The corresponding Lebesgue constants are of optimal order.
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Additional Information
  • Sven Ehrich
  • Affiliation: Universität Hildesheim, Institut für Mathematik, D–31141 Hildesheim, Germany
  • Email: ehrich@informatik.uni-hildesheim.de
  • Giuseppe Mastroianni
  • Affiliation: Università degli Studi della Basilicata, Dipartimento di Matematica, I–85100 Potenza, Italy
  • Email: mastroianni@pzvx85.cineca.it
  • Received by editor(s): June 20, 1995
  • Received by editor(s) in revised form: December 4, 1995
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 311-331
  • MSC (1991): Primary 42A05, 65D05
  • DOI: https://doi.org/10.1090/S0025-5718-97-00808-9
  • MathSciNet review: 1388888