Dynamic Deflation For Implicitly Restarted Block Lanczos Method

In order to compute the multiple or clustered eigenvalues effectively, a dynamic deflation technique for the implicitly restarted block Lanczos method is presented, and its application to the implicitly restarted block Lanczos method is discussed.The implicitly restarted block Lanczos method is the polynomial acceleration method. The rate of convergence depends on the choice of shifts. This paper proposes a new shift selection strategy. In order to increase the convergence and stability, we propose two deflation strategies, locking and purging. If the converged Ritz values is wanted, it is necessary to keep it in the subsequent of block Lanczos factorizations. This is called locking. If the converged Ritz value is unwanted then it must be removed from the subsequent of block Lanczos factorizations. This is called purging.A few of cases are compared in numerical experiments. Numerical results show the dynamic deflation for the implicitly restarted block Lanczos method is effective for computing the multiple or clustered eigenvalues of a large sparse symmetric matrix.