Block Jacobi-Davidson Method For Solving Generalized Symmetirc Eigenvalue Problems

Jacobi-Davidson method is very efficient for computing the extreme eigenpairs of the generalized symmetric eigenproblems. This paper presents the block version of the method and applies the harmonic strategy to the block Jacobi-Davidson method, then derives the harmonic block Jacobi-Davidson method by which the multiple or clustered interior eigenvalues of the generalized symmetric eigenproblems can be computed efficiently. To approximate the correction vectors efficiently, the preconditioning technique of the correction equation is considered. Moreover, in order to reduce the computational cost and storage of the method, the restarting and deflation techniques are discussed. Numerical experiments show that the block Jacobi-Davidson method is efficient for computing the multiple or clustered extreme eigenpairs and the harmonic block Jacobi-Davidson method is efficient for computing the interior eigenpairs of the generalized symmetric eigenproblems.