To compute the optimal interpolation formula

Gaffney, P. W.

doi:10.1090/S0025-5718-1978-0474698-2

To compute the optimal interpolation formula
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Math. Comp. 32 (1978), 763-777 Request permission

Abstract:

The purpose of this paper is to explain how to compute the function $\Omega$ which interpolates values of a function of one variable $f(x)$ at n distinct points ${x_1} < {x_2} < \cdots < {x_{n - 1}} < {x_n}$ and which, whenever $\left \|{f^{(k)}}\right \|_\infty$ is bounded and the value of the bound is unknown, provides the smallest possible value of $B(x)$ in the error bound \[ |f(x) - \Omega (x)| \leqslant B(x)\left \|{f^{(k)}}\right \|_{\infty .}\]

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Optimal Interpolation

The Range of Possible Values of

Fortran Subroutines for Computing the Optimal Interpolation Formula

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Interpolation