A generalized Nyström method with subspace iteration for low-rank approximations of large-scale nonsymmetric matrices

Abstract

In numerical linear algebra, finding the low-rank approximation of large-scale nonsymmetric matrices is a core problem. In this work, we combine the generalized Nyström method and randomized subspace iteration to propose a new low-rank approximation algorithm, which we refer to as the generalized Nyström method with subspace iteration. Moreover, utilizing the projection theory, we perform an in-depth error analysis from a novel perspective and establish the theoretical error bound of the proposed algorithm. Finally, numerical experiments show that our method outperforms the randomized singular value decomposition and generalized Nyström method in accuracy, especially when applied to a matrix with slowly decaying singular values.