Speaker
Description
We present and analyze a new randomized algorithm called rand-cholQR
for computing tall-and-skinny QR factorizations.
Using one or two random sketch matrices, it is proved that with
high probability, its orthogonality error is bounded by a constant
of the order of unit roundoff for any numerically full-rank matrix.
An evaluation of the performance of rand-cholQR on a NVIDIA A100 GPU
demonstrates that for tall-and-skinny matrices, rand-cholQR with
multiple sketch matrices is nearly as fast as, or in some cases faster
than, the state-of-the-art CholeskyQR2. Hence, compared to CholeskyQR2,
rand-cholQR is more stable with almost no extra computational or
memory cost, and therefore a superior algorithm both in theory and practice.
Joint work with Andrew J. Higgins, Erik Boman, and Yichitaro Yamazaki
