Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Certifying solutions to square systems of polynomial-exponential
  equations   Smale's alpha-theory certifies that Newton iterations will converge
quadratically to a solution of a square system of analytic functions based on
the Newton residual and all higher order derivatives at the given point. Shub
and Smale presented a bound for the higher order derivatives of a system of
polynomial equations based in part on the degrees of the equations. For a given
system of polynomial-exponential equations, we consider a related system of
polynomial-exponential equations and provide a bound on the higher order
derivatives of this related system. This bound yields a complete algorithm for
certifying solutions to polynomial-exponential systems, which is implemented in
alphaCertified. Examples are presented to demonstrate this certification
algorithm.

34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics