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Abel — Gontscharoff Interpolation

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Error Inequalities in Polynomial Interpolation and Their Applications

Part of the book series: Mathematics and Its Applications ((MAIA,volume 262))

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Abstract

Let —∞ < a < b < ∞, and a ≤ a 1 ≤ a 2 ≤ … ≤ a n ≤ b be the given points. It is easily seen that the Abel 7#x2014; Gontscharoff interpolating polynomial P (3.1.1)(t) of degree (n − 1) satisfying the Abel — Gontscharoff conditions

$$ P_{(3.1.1)}^{(i)} (a_{i + 1} ) = A_{i + 1} ,0 \leqslant i \leqslant n - 1 $$
(3.1.1)

exists uniquely [10,15].

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Kent Ridge, Singapore

    Ravi P. Agarwal

  2. Division of Mathematics, Nanyang Technological University, Singapore

    Patricia J. Y. Wong

Authors
  1. Ravi P. Agarwal
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  2. Patricia J. Y. Wong
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© 1993 Springer Science+Business Media Dordrecht

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Agarwal, R.P., Wong, P.J.Y. (1993). Abel — Gontscharoff Interpolation. In: Error Inequalities in Polynomial Interpolation and Their Applications. Mathematics and Its Applications, vol 262. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2026-5_3

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  • DOI: https://doi.org/10.1007/978-94-011-2026-5_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4896-5

  • Online ISBN: 978-94-011-2026-5

  • eBook Packages: Springer Book Archive

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