A new restarting method in the harmonic projection algorithm for computing the eigenvalues of a nonsymmetric matrix
The harmonic projection method can be used to find interior eigenpairs of large matrices. Given a target point or shift τ to which the needed interior eigenvalues are close, the desired interior eigenpairs are the eigenvalues nearest τ and the associated eigenvectors. 
 
However, it has been shown that the harmonic projection method may converge erratically and even may fail to do so. In this paper, we present a new restarting method in the harmonic projection algorithm for computing the eigenvalues of a nonsymmetric matrix. The implementation of the algorithm has been tested by numerical examples, the results show that the algorithm converges fast and works with high accuracy.