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Article overview
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Fitting a Sobolev function to data | | Charles L. Fefferman
; Arie Israel
; Garving K. Luli
; | | Date: |
6 Nov 2014 | | Abstract: | We exhibit an algorithm to solve the following extension problem: Given a
finite set $E subset mathbb{R}^n$ and a function $f: E
ightarrow
mathbb{R}$, compute an extension $F$ in the Sobolev space
$L^{m,p}(mathbb{R}^n)$, $p>n$, with norm having the smallest possible order of
magnitude, and secondly, compute the order of magnitude of the norm of $F$.
Here, $L^{m,p}(mathbb{R}^n)$ denotes the Sobolev space consisting of functions
on $mathbb{R}^n$ whose $m$th order partial derivatives belong to
$L^p(mathbb{R}^n)$. The running time of our algorithm is at most $C N log N$,
where $N$ denotes the cardinality of $E$, and $C$ is a constant depending only
on $m$,$n$, and $p$. | | Source: | arXiv, 1411.1786 | | Services: | Forum | Review | PDF | Favorites | |
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