The Range of Possible Values of f(x)

1 March 1978

journal article
research article
Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics

Vol. 21 (2) , 211-226
https://doi.org/10.1093/imamat/21.2.211

Abstract

The purpose of this paper is to explain how to compute the range of possible values of a function of one variable, f(x), given values of the function at n distinct points x₁ < x₂ < … < x_M−1 < x_M, and given a finite bound on the kth derivative of f: ∥f^(k)∥_∞ ≤ L, 1 ≤ k ≤ n.

Keywords

FUNCTION
SUP
TH DERIVATIVE
FINITE BOUND
DISTINCT POINTS

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