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Each iteration in Jacobi-Davidson method for solving large sparse eigenvalueproblems involves two phases, called subspace expansion and eigen pairextraction. The subspace expansion phase involves solving a correctionequation. We propose a modification to this by introducing a related correctionequation, motivated by the least squares. We call the proposed method as theModified Jacobi-Davidson Method. When the subspace expansion is ignored as inthe Simplified Jacobi- Davidson Method, the modified method is called asModified Simplified Jacobi-Davidson Method. We analyze the convergenceproperties of the proposed method for Symmetric matrices. Numerical experimentshave been carried out to check whether the method is computationally viable ornot.

A modification of the Jacobi-Davidson method