Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local and global geometry of Prony systems and Fourier reconstruction of
  piecewise-smooth functions   Many reconstruction problems in signal processing require solution of a
certain kind of nonlinear systems of algebraic equations, which we call Prony
systems. We study these systems from a general perspective, addressing
questions of global solvability and stable inversion. Of special interest are
the so-called "near-singular" situations, such as a collision of two closely
spaced nodes.
  We also discuss the problem of reconstructing piecewise-smooth functions from
their Fourier coefficients, which is easily reduced by a well-known method of
K.Eckhoff to solving a particular Prony system. As we show in the paper, it
turns out that a modification of this highly nonlinear method can reconstruct
the jump locations and magnitudes of such functions, as well as the pointwise
values between the jumps, with the maximal possible accuracy.

23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th