Componentwise perturbation analyses for the QR factorization

@article{Chang2001ComponentwisePA,
  title={Componentwise perturbation analyses for the QR factorization},
  author={Xiao-Wen Chang and Christopher C. Paige},
  journal={Numerische Mathematik},
  year={2001},
  volume={88},
  pages={319-345}
}
This paper gives componentwise perturbation analyses for Q andR in the QR factorizationA = QR,QTQ = I,R upper triangular, for a given real m×nmatrixA of rankn. Such specific analyses are important for examplewhen the columnsof Aare badly scaled. First order perturbation bounds are given for both Q andR. The analyses more accurately reflect the sensitivity of the problem than previous such results. The condition number forR is bounded for a fixedn when the standard column pivoting strategy is… CONTINUE READING
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