Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining system poles using row sequences of orthogonal
  Hermite-Pad\'e approximants   Given a system of functions $\textup{\textbf{F}}=(F_1,\ldots,F_d),$ analytic
on a neighborhood of some compact subset $E$ of the complex plane with simply
connected complement, we define a sequence of vector rational functions with
common denominator in terms of the orthogonal expansions of the components
$F_k, k=1,\ldots,d,$ with respect to a sequence of orthonormal polynomials
associated with a measure $\mu$ whose support is contained in $E$. Such
sequences of vector rational functions resemble row sequences of type II
Hermite-Pad\'e approximants. Under appropriate assumptions on $\mu,$ we give
necessary and sufficient conditions for the convergence with geometric rate of
the common denominators of the sequence of vector rational functions so
constructed. The exact rate of convergence of these denominators is provided
and the rate of convergence of the simultaneous approximants is estimated. It
is shown that the common denominator of the approximants detect the location of
the poles of the system of functions.

18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex