Abstract
The QR factorization is one of the most important and useful matrix factorizations in scientific computing. A recent communication-avoiding version of the tall-and-skinny QR factorization is ideal to compute the R matrix in a QR factorization on MapReduce, an environment where computationally intensive processes operate on small subsets of a large database. Getting the Q factor in a stable manner is more difficult. We present a few implementations of the tall-and-skinny QR (TSQR) factorization in the MapReduce framework and pay particular attention to the numerical stability of the procedure. As a byproduct, we can used the RSVD procedure to compute the SVD of tall-and-skinny matrices as well. We discuss some applications to simulation data analysis and reduced order modeling.