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In this work we generalize the Jacobi-Davidson method to the case wheneigenvector can be reshaped into a low-rank matrix. In this setting theproposed method inherits advantages of the original Jacobi-Davidson method, haslower complexity and requires less storage. We also introduce low-rank versionof the Rayleigh quotient iteration which naturally arises in theJacobi-Davidson method.

Jacobi-Davidson method on low-rank matrix manifolds