Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fitting a Sobolev function to data   We exhibit an algorithm to solve the following extension problem: Given a
finite set $E \subset \mathbb{R}^n$ and a function $f: E \rightarrow
\mathbb{R}$, 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 $p$.

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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
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The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph