A thorough backward stability analysis of Hotelling's 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.

翻译：对Hotelling通缩进行彻底的后向稳定分析,这是通过低调更新来计算对称矩阵许多成份的低位更新而明确的外部通缩程序。计算出计算成的成份精度的折向性损失的可计算上限和计算成的成份成份的对称后向错误规范的可计算上限。显露出明确的外部通缩程序的后向稳定所需的充分条件。根据这些理论结果,提出了通过动态选择变换实现数字后向稳定的战略。数字结果将用来证实理论分析,并表明从应用中生成的大型对称矩阵计算许多成份的成份程序是否稳定。