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Register a new userBackward Stability of Explicit External Deflation for the Symmetric Eigenvalue Problem
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Added by
Chao-Ping Lin
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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A thorough backward stability analysis of Hotellings deflation, an explicit external deflation procedure through low-rank updates for computing many eigenpairs of a symmetric matrix, is presented. Computable upper bounds of the loss of the orthogonality of the computed eigenvectors and the symmetric backward error norm of the computed eigenpairs are derived. Sufficient conditions for the backward stability of the explicit external deflation procedure are revealed. Based on these theoretical results, the strategy for achieving numerical backward stability by dynamically selecting the shifts is proposed. Numerical results are presented to corroborate the theoretical analysis and to demonstrate the stability of the procedure for computing many eigenpairs of large symmetric matrices arising from applications.
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