On the Failure of Rank-Revealing QR Factorization Software - A Case Study

@article{Drmac2006OnTF,
  title={On the Failure of Rank-Revealing QR Factorization Software - A Case Study},
  author={Zlatko Drmac and Zvonimir Bujanovic},
  journal={ACM Trans. Math. Softw.},
  year={2006},
  volume={35},
  pages={12:1-12:28}
}
This article reports an unexpected and rather erratic behavior of the LAPACK software implementation of the QR factorization with Businger-Golub column pivoting. It is shown that, due to finite precision arithmetic, the software implementation of the factorization can catastrophically fail to produce a properly structured triangular factor, thus leading to a potentially severe underestimate of a matrix's numerical rank. The 30-year old problem, dating back to LINPACK, has (undetectedly) badly… CONTINUE READING

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