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 wk+1,…,wmwk+1,…,wm of AA from the orthogonal complement of span of those wanted harmonic Ritz vectors with respect to Km(A,v1)Km(A,v1), then present an implicitly restarted harmonic Arnoldi algorithm with wk+1,…,wmwk+1,…,wm 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.