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This paper proposes an approach to accelerate local, linear iterative network algorithms asymptotically achieving distributed average consensus. We focus on the class of algorithms in which each node initializes its ldquostate valuerdquo to the local measurement and then at each iteration of the algorithm, updates this state value by adding a weighted sum of its own and its neighbors' state values. Provided the weight matrix satisfies certain convergence conditions, the state values asymptotically converge to the average of the measurements, but the convergence is generally slow, impeding the practical application of these algorithms. In order to improve the rate of convergence, we propose a novel method where each node employs a linear predictor to predict future node values. The local update then becomes a convex (weighted) sum of the original consensus update and the prediction; convergence is faster …