  The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz
algorithm to the situation in which data is distributed throughout a network
represented by a tree. We isolate substructures of the network and study
convergence of the distributed Kazmarz algorithm for relatively large
relaxation parameters associated to these substructures. If the system is
consistent, then the algorithm converges to the solution of minimal norm;
however, if the system is inconsistent, then the algorithm converges to an
approximated least-squares solution that is dependent on the parameters and the
network topology. We show that the relaxation parameters may be larger than the
standard upper-bound in literature in this context and provide numerical
experiments to support our results.
