Title: A Distributed Algorithm for Computing a Common Fixed Point of a Finite Family of Paracontractions,
Abstract: A distributed algorithm is described for finding a common fixed point of a
family of m>1 nonlinear maps M_i : R^n -> R^n assuming that each map is a
paracontraction and that at least one such 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 a
fixed point by utilizing the current estimates generated by each of its
neighbors. Neighbor relations are characterized by a time-varying directed
graph N(t). It is shown under suitably general conditions on N(t), that the
algorithm causes all agents estimates to converge to the same common fixed
point of the m nonlinear maps.