  Each iteration in Jacobi-Davidson method for solving large sparse eigenvalue
problems involves two phases, called subspace expansion and eigen pair
extraction. The subspace expansion phase involves solving a correction
equation. We propose a modification to this by introducing a related correction
equation, motivated by the least squares. We call the proposed method as the
Modified Jacobi-Davidson Method. When the subspace expansion is ignored as in
the Simplified Jacobi- Davidson Method, the modified method is called as
Modified Simplified Jacobi-Davidson Method. We analyze the convergence
properties of the proposed method for Symmetric matrices. Numerical experiments
have been carried out to check whether the method is computationally viable or
not.
