### Abstract

Given positive integers m, n, and p, where m ≥ n+p and p ∗ n. A method is proposed to modify the QR decomposition of X ∈ ℝ^{m × n} to produce a QR decomposition of X with p rows deleted. The algorithm is based upon the classical block Gram-Schmidt method, requires an approximation of the norm of the inverse of a triangular matrix, has O(mnp) operations, and achieves an accuracy in the matrix 2-norm that is comparable to similar bounds for related procedures for p = 1 in the vector 2-norm. Since the algorithm is based upon matrixmatrix operations, it is appropriate for modern cache oriented computer architectures.

Original language | English (US) |
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Pages (from-to) | 163-187 |

Number of pages | 25 |

Journal | Electronic Transactions on Numerical Analysis |

Volume | 43 |

State | Published - Jan 1 2014 |

### All Science Journal Classification (ASJC) codes

- Analysis

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## Cite this

Barlow, J. L. (2014). Block gram-schmidt downdating.

*Electronic Transactions on Numerical Analysis*,*43*, 163-187.