  In this paper, we investigate the convergence performance of a cooperative
diffusion Gauss-Newton (GN) method, which is widely used to solve the nonlinear
least squares problems (NLLS) due to the low computation cost compared with
Newton's method. This diffusion GN collects the diversity of temporalspatial
information over the network, which is used on local updates. In order to
address the challenges on convergence analysis, we firstly consider to form a
global recursion relation over spatial and temporal scales since the
traditional GN is a time iterative method and the network-wide NLLS need to be
solved. Secondly, the derived recursion related to the networkwide deviation
between the successive two iterations is ambiguous due to the uncertainty of
descent discrepancy in GN update step between two versions of cooperation and
non-cooperation. Thus, an important work is to derive the boundedness
conditions of this discrepancy. Finally, based on the temporal-spatial
recursion relation and the steady-state equilibria theory for discrete
dynamical systems, we obtain the sufficient conditions for algorithm
convergence, which require the good initial guesses, reasonable step size
values and network connectivity. Such analysis provides a guideline for the
applications based on this diffusion GN method.
