  We study the Principal Component Analysis (PCA) problem in the distributed
and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a
rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we
want to output an $m \times k$ orthonormal matrix $U$ for which $$ || A - U U^T
A ||_F^2 \le \left(1 + \epsilon \right) \cdot || A - A_k||_F^2, $$ where $A_k
\in R^{m \times n}$ is the best rank-$k$ approximation to $A$.
  This paper provides improved algorithms for distributed PCA and streaming
PCA.
