Computing rank‐revealing factorizations of matrices stored out‐of‐core

This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external devices such as disks (out-of-core or out-of-memory). Traditional (such the column pivoted QR factorization singular value decomposition) very communication intensive they require many vector-vector matrix-vector operations, which become prohibitively expensive when data is not RAM. Randomization allows reformulate new methods so contiguous blocks matrix processed bulk. The two distinct methods. first a blocked version Householder QR, organized “left-looking” method minimize number write operations. second results employs UTV factorization. It an algorithm-by-blocks overlap computations I/O As it incorporates power iterations, much better at revealing numerical rank. Numerical experiments several computers demonstrate almost fast processing traditional