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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • Giuseppe Mastroianni
  • Affiliation: Università degli Studi della Basilicata, Dipartimento di Matematica, I–85100 Potenza, Italy
  • Email:
  • 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:
  • MathSciNet review: 1388888