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Mathematics of Computation

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To compute the optimal interpolation formula

Author: P. W. Gaffney
Journal: Math. Comp. 32 (1978), 763-777
MSC: Primary 65D05
MathSciNet review: 0474698
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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\Vert{f^{(k)}}\right\Vert _\infty $ is bounded and the value of the bound is unknown, provides the smallest possible value of $ B(x)$ in the error bound

$\displaystyle \vert f(x) - \Omega (x)\vert \leqslant B(x)\left\Vert{f^{(k)}}\right\Vert _{\infty .}$

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Article copyright: © Copyright 1978 American Mathematical Society

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