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Fitting a Sobolev function to data I

Author(s): Fefferman, Charles L.; Israel, Arie; Luli, Garving

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Abstract: In this paper and two companion papers, we produce efficient algorithms to solve the following interpolation problem: Let m >= 1 and p > n >= 1. Given a finite set E subset of R-n and a function f : E -> R, compute an extension F of f belonging to the Sobolev space W-m,W-p (R-n) with norm having the smallest possible order of magnitude; secondly, compute the order of magnitude of the norm of F. The combined running time of our algorithms is at most CN log N, where N denotes the cardinality of E, and C depends only on m, n, and p.
Publication Date: 2016
Electronic Publication Date: 29-Feb-2016
Citation: Fefferman, Charles, Israel, Arie, Luli, Garving. (2016). Fitting a Sobolev function to data I. REVISTA MATEMATICA IBEROAMERICANA, 32 (275 - 376. doi:10.4171/RMI/887
DOI: doi:10.4171/RMI/887
ISSN: 0213-2230
Pages: 275 - 376
Type of Material: Journal Article
Version: Author's manuscript

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