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We propose a general framework for reconstructing and denoising singleentries of incomplete and noisy entries. We describe: effective algorithms fordeciding if and entry can be reconstructed and, if so, for reconstructing anddenoising it; and a priori bounds on the error of each entry, individually. Inthe noiseless case our algorithm is exact. For rank-one matrices, the newalgorithm is fast, admits a highly-parallel implementation, and produces anerror minimizing estimate that is qualitatively close to our theoretical andthe state-of-the-are Nuclear Norm and OptSpace methods.

Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion