A thorough backward stability analysis of Hotelling’s deflation, an explicitexternal deflation procedure through low-rank updates for computing manyeigenpairs of a symmetric matrix, is presented . Computable upper bounds of theloss of the orthogonality and the symmetricbackward error norm of the computed eigenvectors are derived . Sufficientconditions for the backward stability of the explicit external deflationprocedure are revealed . The strategy forachieving numerical backward stability by dynamically selecting the shifts is proposed .

Author(s) : Chao-Ping Lin, Ding Lu, Zhaojun Bai

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Keywords : stability - deflation - symmetric - explicit - external -

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