Recent development for computing singular values of a generalized tensor sum

Abstract

In this paper, the recent progress of computing singular values of a generalized tensor sum is described. To be specific, the already-known algorithms are classified into three groups: to compute the maximum and minimum singular values, the minimum singular values only, and an arbitrary singular value. All the algorithms are constructed over tensor space, leading to largely memory-efficient. Among them, regarding the speed of convergence, the algorithm for maximum and minimum singular values still has room to be improved for non-symmetric generalized tensor sum by some suitable choices of the initial guess. Considering the tensor structure of the initial guess, we experimentally show that some new initial guesses are efficient for computing the maximum and minimum singular values.