Jacobi-Davidson method on low-rank matrix manifolds
It provides a more efficient eigenvector computation for problems where eigenvectors have low-rank structure, which is common in applications like matrix completion and recommender systems.
The paper generalizes the Jacobi-Davidson method to compute eigenvectors that are low-rank matrices, achieving lower complexity and reduced storage compared to the standard method.
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.