A new restarting method in the Lanczos algorithm for generalized eigenvalue problem

In this paper, we present a new restarting method in the Lanczos algorithm for computing a few eigenvalues of the symmetric positive definite eigenvalue problem, AX = λBX, where A and B are large and sparse matrices.The implementation of the algorithm has been tested by numerical examples, the results show that the algorithm converges fast and works with high accuracy.