Revista Matemática Iberoamericana


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Volume 28, Issue 2, 2012, pp. 415–533
DOI: 10.4171/rmi/683

Published online: 2012-04-22

Nearly optimal interpolation of data in $C^2 (\mathbb{R}^2)$. Part I

Charles Fefferman[1]

(1) Princeton University, United States

Given $\epsilon > 0$, we compute a function taking prescribed values at $N$ given points in $\mathbb{R}^2$, whose $C^2$-norm is within a factor $(1 + \epsilon)$ of least possible. The computation takes $C ( \epsilon ) N \log N$ computer operations.

Keywords: Interpolation, $C^2$-norm, efficient algorithm

Fefferman Charles: Nearly optimal interpolation of data in $C^2 (\mathbb{R}^2)$. Part I. Rev. Mat. Iberoamericana 28 (2012), 415-533. doi: 10.4171/rmi/683