Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform approximation on the sphere by least squares polynomials   The paper concerns the uniform polynomial approximation of a function $f$,
continuous on the unit Euclidean sphere of ${\mathbb R}^3$ and known only at a
finite number of points that are somehow uniformly distributed on the sphere.
First we focus on least squares polynomial approximation and prove that the
related Lebesgue constants w.r.t. the uniform norm grow at the optimal rate.
Then, we consider delayed arithmetic means of least squares polynomials whose
degrees vary from $n-m$ up to $n+m$, being $m=\lfloor \theta n\rfloor$ for any
fixed parameter $0<\theta<1$. As $n$ tends to infinity, we prove that these
polynomials uniformly converge to $f$ at the near-best polynomial approximation
rate. Moreover, for fixed $n$, by using the same data points we can further
improve the approximation by suitably modulating the action ray $m$ determined
by the parameter $\theta$. Some numerical experiments are given to illustrate
the theoretical results.

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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph