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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The degree of piecewise monotone interpolation
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by Eli Passow and Louis Raymon PDF
Proc. Amer. Math. Soc. 48 (1975), 409-412 Request permission

Abstract:

Let $0 = {x_0} < {x_1} < \cdots < {x_k} = 1$ and let ${y_0},{y_1}, \cdots ,{y_k}$ be real numbers such that ${y_{j - 1}} \ne {y_j},j = 1,2, \cdots ,k$. Estimates are obtained on the degree of an algebraic polynomial $p(x)$ that interpolates the given data piecewise monotonely; i.e., such that (i) $p({x_j}) = {y_j},j = 0,1, \cdots ,k$, and such that (ii) $p(x)$ is increasing on ${I_j} = ({x_{j - 1}},{x_j}{\text {) if }}{y_j} < {y_{j - 1}}$, and decreasing on ${I_j}$. if ${y_j} < {y_{j - 1}},j = 1,2, \cdots ,k$. The problem is seen to be related to the problem of monotone approximation.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 409-412
  • MSC: Primary 41A15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0430608-4
  • MathSciNet review: 0430608