Geodesic
Block Gram-Schmidt downdating
Electronic transactions on numerical analysis, Tome 43 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {43},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__43__a2/}
}
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%J Electronic transactions on numerical analysis
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Barlow, Jesse L. Block Gram-Schmidt downdating. Electronic transactions on numerical analysis, Tome 43 (2015). http://geodesic.mathdoc.fr/item/ETNA_2015__43__a2/