Geodesic
Block Gram-Schmidt downdating
Electronic transactions on numerical analysis, Tome 43 (2015)
Given positive integers $m, n$, and $p,$ where $m \geq n+p$ and $p \ll n$. A method is proposed to modify the QR decomposition of $X \in \mathbb{R}^{m \times n}$ 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 $\mathcal{O}(mnp)$ 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 matrix-matrix operations, it is appropriate for modern cache oriented computer architectures.
Classification : 65F25, 65F20, 65F35
Keywords: QR decomposition, singular value decomposition, orthogonality, downdating, matrix-matrix operations 
@article{ETNA_2015__43__a2,
     author = {Barlow,  Jesse L.},
     title = {Block {Gram-Schmidt} downdating},
     journal = {Electronic transactions on numerical analysis},
     year = {2015},
     volume = {43},
     zbl = {1312.65066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__43__a2/}
}
TY  - JOUR
AU  - Barlow,  Jesse L.
TI  - Block Gram-Schmidt downdating
JO  - Electronic transactions on numerical analysis
PY  - 2015
VL  - 43
UR  - http://geodesic.mathdoc.fr/item/ETNA_2015__43__a2/
LA  - en
ID  - ETNA_2015__43__a2
ER  - 
%0 Journal Article
%A Barlow,  Jesse L.
%T Block Gram-Schmidt downdating
%J Electronic transactions on numerical analysis
%D 2015
%V 43
%U http://geodesic.mathdoc.fr/item/ETNA_2015__43__a2/
%G en
%F ETNA_2015__43__a2
Barlow,  Jesse L. Block Gram-Schmidt downdating. Electronic transactions on numerical analysis, Tome 43 (2015). http://geodesic.mathdoc.fr/item/ETNA_2015__43__a2/