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This paper introduces algorithms for the decentralized low-rank matrix completion problem. Assume a low-rank matrix W = [W ₁ ,W ₂ , ...,W _L ]. In a network, each agent observes some entries of W  . In order to recover the unobserved entries of W via decentralized computation, we factorize the unknown matrix W as the product of a public matrix X, common to all agents, and a private matrix Y = [Y ₁ ,Y ₂ , ...,Y _L ], where Y  is held by agent . Each agent alternatively updates Y  and its local estimate of X while communicating with its neighbors toward a consensus on the estimate. Once this consensus is (nearly) reached throughout the network, each agent recovers W  = XY  , and thus W is recovered. The communication cost is scalable to the number of agents, and W  and Y  are kept private to agent to a certain extent. The algorithm is accelerated by extrapolation and compares favorably to the centralized

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