Efficient algorithms for computing rank‐revealing factorizations on a GPU

Standard rank-revealing factorizations such as the singular value decomposition (SVD) and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is inability of standard algorithms cast most operations terms Level-3 BLAS. This article presents two alternative for computing form = U T V ∗ $$ \mathbf{\mathsf{A}}=\mathbf{\mathsf{UT}}{\mathbf{\mathsf{V}}}^{\ast } , where \mathbf{\mathsf{U}} \mathbf{\mathsf{V}} orthogonal \mathbf{\mathsf{T}} trapezoidal (or triangular if \mathbf{\mathsf{A}} square). Both use randomized projection techniques flops matrix-matrix multiplication, which exceptionally efficient Numerical experiments illustrate that these achieve significant acceleration over finely tuned GPU implementations SVD while providing low rank approximation errors close SVD.