Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization

@article{Gu1996EfficientAF,
  title={Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization},
  author={Ming Gu and Stanley C. Eisenstat},
  journal={SIAM J. Scientific Computing},
  year={1996},
  volume={17},
  pages={848-869}
}
Given an m n matrix M with m > n, it is shown that there exists a permutation FI and an integer k such that the QR factorization MYI= Q(Ak ckBk) reveals the numerical rank of M: the k k upper-triangular matrix Ak is well conditioned, IlCkll2 is small, and Bk is linearly dependent on Ak with coefficients bounded by a low-degree polynomial in n. Existing rank-revealing QR (RRQR) algorithms are related to such factorizations and two algorithms are presented for computing them. The new algorithms… CONTINUE READING

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Methods for modifying matrix factorizations

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