On the Imprecise Solution to Block Jacobi-Davidson Method for Large Real Symmetric Eigenvalue Problems

The block Jacobi-Davidson method is effective for computing large scale real symmetric eigenvalue problems,the issues addressed being the multiple or clustered eigenpairs.The block Jacobi-Davidson method includes outer and inner iterative.The outer iterative is used to compute the pairs of eigenvalues while the inner iterative is used for the correction equations.The more time-consuming computation lies in solving the correction equations.To handle the imprecise solution of the correction equation,we propose several block incomplete factorization methods to obtain the pre-conditioning matrix.Numerical experiments were also carried out to compare the effect of these methods.