A study on parallelization of successive rotation based joint diagonalization

Joint diagonalization (JD) is an instrumental tool in a vast variety of applications such as blind source separation, polarization sensitive array processing, and linear algebra based computation of tensor decompositions. Among the JD families, those based on successive rotations are a major category that minimizes the adopted highly nonlinear cost function by solving a set of simple sub-optimization problems. These sub-optimization problems are associated with certain elementary rotations that are performed over one or two rows and columns of target matrices, and thus a lower-dimensional exhaustion is required to cover and update all the matrix entries in a sequential manner. As such, the time consumed in the exhaustion procedure is in quadratic relationship with the dimensionality of target matrices and would go extremely heavy when handling large matrices. In this study, we examine and compare 3 parallelization schemes for a recently developed successive rotation based JD algorithm. The results show that these schemes can largely reduce the running time of JD with almost equal resulting accuracy when compared with the original version, when handling large matrices.