Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures

Understand

The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis.

• For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a numerically stable, efficient, communication-avoiding algorithm for computing the QR factorization.
• It has been used in traditional high performance computing and grid computing environments.
• For MapReduce environments, existing methods to compute the QR decomposition use a numerically unstable approach that relies on indirectly computing the Q factor.