A single pass randomized algorithm for the approximate eigenvalue de - composition

Recall that in Lecture 13, a randomized algorithm was described for computing a low rank approximation to the eigendecomposition of a matrix A. A drawback to this method is that the matrix A must be accessed multiple times (twice), which may not be possible in streaming models where A cannot be stored in memory [1]. For the streaming model, we require a single pass algorithm, where A is accessed only once. To derive this algorithm, we begin with a brief review of the multipass method, and work under the assumption that A ∈ Rn×n is a symmetric matrix.