Jacobi--Davidson Method on Low-Rank Matrix Manifolds

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