A new shift scheme for the harmonic Arnoldi method

The implicitly restarted harmonic Arnoldi algorithm by Morgan used those unwanted harmonic Ritz values as shifts—called Morgan’s harmonic shifts. In this paper, a new shift scheme is given for the harmonic Arnoldi algorithm. We first analyze the harmonic Ritz values w k + 1 , … , w m of A from the orthogonal complement of span of those wanted harmonic Ritz vectors with respect to K m ( A , v 1 ) , then present an implicitly restarted harmonic Arnoldi algorithm with w k + 1 , … , w m as shifts. Finally, through the numerical experiments, we mainly draw comparisons on our algorithm and Morgan’s algorithm, and show our algorithm often performed better than Morgan’s one.