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A distributed algorithm is described for solving a linear algebraic equation of the form Ax = b where A is a matrix for which the equation has at least one solution. The equation is simultaneously solved by m agents assuming each agent knows only a subset of the rows of the partitioned matrix [A b], the current estimates of the equation's solution generated by its neighbors, and nothing more. Each...
This paper investigates accelerated gossip algorithms for distributed computations in networks where shift-registers are utilized at each node. By using tools from matrix analysis, we prove the existence of the desired acceleration and establish the fastest rate of convergence in expectation for two-register symmetric gossip. Some classes of networks with regular graph topologies are studied in detail...
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