Faster Subset Selection for Matrices and Applications

@article{Avron2011FasterSS,
  title={Faster Subset Selection for Matrices and Applications},
  author={Haim Avron and Christos Boutsidis},
  journal={SIAM J. Matrix Analysis Applications},
  year={2011},
  volume={34},
  pages={1464-1499}
}
We study subset selection for matrices defined as follows: given a matrix $\matX \in \R^{n \times m}$ ($m > n$) and an oversampling parameter $k$ ($n \le k \le m$), select a subset of $k$ columns from $\matX$ such that the pseudo-inverse of the subsampled matrix has as smallest norm as possible. In this work, we focus on the Frobenius and the spectral matrix norms. We describe several novel (deterministic and randomized) approximation algorithms for this problem with approximation bounds that… CONTINUE READING

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