Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An adaptive partition of unity method for multivariate Chebyshev
  polynomial approximations   Spectral polynomial approximation of smooth functions allows real-time
manipulation of and computation with them, as in the Chebfun system. Extension
of the technique to two-dimensional and three-dimensional functions on
hyperrectangles has mainly focused on low-rank approximation. While this method
is very effective for some functions, it is highly anisotropic and unacceptably
slow for many functions of potential interest. A method based on automatic
recursive domain splitting, with a partition of unity to define the global
approximation, is easy to construct and manipulate. Experiments show it to be
as fast as existing software for many low-rank functions, and much faster on
other examples, even in serial computation. It is also much less sensitive to
alignment with coordinate axes. Some steps are also taken toward approximation
of functions on nonrectangular domains, by using least-squares polynomial
approximations in a manner similar to Fourier extension methods, with promising
results.

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess