Problem 34: Linear Algebra Computation

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Suggested by Michael Mahoney
Source Kanpur 2009
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It is often not the case that the entire data sits on a single machine and that we are allowed to make one or more passes over it. Instead the data is often distributed across multiple systems. This is one of the reasons why the streaming model does not have more impact in practice for linear algebra computation. It would be great to design new models that address this shortcoming.

Consider also the following problem. Let $A$ be an $m\times n$ matrix and let $k$ be a rank parameter. Let $P_{A,k}$ be the projection matrix on the best rank-$k$ left (or right) singular subspace. The goal is to compute the diagonal of $P_{A,k}$ exactly or approximately in a small number of passes in the streaming model, or even better, in a new model that addresses the aforementioned shortcoming.