Jacobi-Davidson method on low-rank matrix manifolds

Abstract

In this work we generalize the Jacobi-Davidson method to the case when eigenvector can be reshaped into a low-rank matrix. In this setting the proposed method inherits advantages of the original Jacobi-Davidson method, has lower complexity and requires less storage. We also introduce low-rank version of the Rayleigh quotient iteration which naturally arises in the Jacobi-Davidson method.

18 pages, 7 figures

References in corpus (1)

• Computation of extreme eigenvalues in higher dimensions using block tensor train format