Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Distributed Algorithm for Computing a Common Fixed Point of a Family
  of Paracontractions   A distributed algorithm is described for finding a common fixed point of a
family of $m>1$ nonlinear maps $M_i : \mathbb{R}^n \rightarrow \mathbb{R}^n$
assuming that each map is a paracontraction and that such a common fixed point
exists. The common fixed point is simultaneously computed by $m$ agents
assuming each agent $i$ knows only $M_i$, the current estimates of the fixed
point generated by its neighbors, and nothing more. Each agent recursively
updates its estimate of the fixed point by utilizing the current estimates
generated by each of its neighbors. Neighbor relations are characterized by a
time-dependent directed graph $\mathbb{N}(t)$ whose vertices correspond to
agents and whose arcs depict neighbor relations. It is shown that for any
family of paracontractions $M_i, i \in \{1,2,\ldots,m\}$ which has at least one
common fixed point, and any sequence of strongly connected neighbor graphs
$\mathbb{N}(t)$, $t=1,2,\ldots$, the algorithm causes all agent estimates to
converge to a common fixed point.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg