# Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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 interpolationHTML articles powered by AMS MathViewer

by Eli Passow and Louis Raymon
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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