Pub Date : 2023-03-30DOI: 10.1109/JMMCT.2023.3263152
Jon T. Kelley;Ali E. Yılmaz;Yaniv Brick
An easy-to-implement iterative algorithm that enables efficient and scalable spectral analysis of dense matrices is presented. The algorithm relies on the approximation of a matrix's singular values by those of a series of smaller matrices formed from uniform random sampling of its rows and columns. It is shown that, for sufficiently incoherent and rank-deficient matrices, the singular values [are expected to] decay at the same rate as those of matrices formed via this sampling scheme, which permits such matrices’ ranks to be accurately estimated from the smaller matrices’ spectra. Moreover, for such a matrix of size $m times n$