Analysis of the SVD Scaling on Large Sparse Matrices

Abstract

There has been great interest in the Singular Value Decomposition (SVD) algorithm over the last years because of its wide applicability in multiple fields of science and engineering, both standalone and as part of other computing methods. The advent of the exascale era with massively parallel computers brings incredible possibilities to deal with very large amounts of data, often stored in a matrix. These advances set the focus on developing better scaling parallel algorithms: e.g., an improved SVD to efficiently factorize a matrix. This study assesses the strong scaling of four SVDs of the SLEPc library, plugged into the PETSc framework to extend its capabilities, via a performance analysis on a population of sparse matrices with up to 109 degrees of freedom. Among them, there is a randomized SVD with promising performance at scale, a key aspect in solvers for exascale simulations since communication must be minimized for scalability success.