A new shift scheme for the harmonic Arnoldi method

Authors:
Guizhi Chen;Jianhua Lin
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China;School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

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.