Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near-optimal sampling strategies for multivariate function approximation
  on general domains   In this paper, we address the problem of approximating a multivariate
function defined on a general domain in $d$ dimensions from sample points. We
consider weighted least-squares approximation in an arbitrary
finite-dimensional space $P$ from independent random samples taken according to
a suitable measure. In general, least-squares approximations can be inaccurate
and ill-conditioned when the number of sample points $M$ is close to $N =
\dim(P)$. To counteract this, we introduce a novel method for sampling in
general domains which leads to provably accurate and well-conditioned
approximations. The resulting sampling measure is discrete, and therefore
straightforward to sample from. Our main result shows near-optimal sample
complexity for this procedure; specifically, $M = \mathcal{O}(N \log(N))$
samples suffice for a well-conditioned and accurate approximation. Numerical
experiments on polynomial approximation in general domains confirm the benefits
of this method over standard sampling.

5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an