Behavior of the Correction Equations in the Jacobi-Davidson Method

The Jacobi-Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi-Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically, the convergence property of the Jacobi-Davidson method influenced by different types of correction equations. As a by-product, we derive the optimal expansion vector, which imposed a shift-and-invert transform on a vector located in the prescribed subspace, to expand the current subspace.