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Keywords:

  • QR factorization;
  • perturbation analysis

SUMMARY

This paper gives normwise and componentwise perturbation analyses for the Q-factor of the QR factorization of the matrix A with full column rank when A suffers from an additive perturbation. Rigorous perturbation bounds are derived on the projections of the perturbation of the Q-factor in the range of A and its orthogonal complement. These bounds overcome a serious shortcoming of the first-order perturbation bounds in the literature and can be used safely. From these bounds, identical or equivalent first-order perturbation bounds in the literature can easily be derived. When A is square and nonsingular, tighter and simpler rigorous perturbation bounds on the perturbation of the Q-factor are presented. Copyright © 2011 John Wiley & Sons, Ltd.