Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination : Proofs and an Extension to Low-rank Approximation ∗

@inproceedings{Pan2015RandomMN,
  title={Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination : Proofs and an Extension to Low-rank Approximation ∗},
  author={Victor Y. Pan and Guoliang Qian and Xiaodong Yan},
  year={2015}
}
We study two applications of standard Gaussian random multipliers. At first we prove that with a probability close to 1 such a multiplier is expected to numerically stabilize Gaussian elimination with no pivoting as well as block Gaussian elimination. Then, by extending our analysis, we prove that such a multiplier is also expected to support low-rank approximation of a matrix without customary oversampling. Our test results are in good accordance with this formal study. The results remain… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 49 references

3

  • M. W. Mahoney, Randomized Algorithms for Matrices, Data, Foundations, Trends in Machine Learning, NOW Publishers
  • 2, 2011. (Abridged version in: Advances in…
  • 2012
Highly Influential
6 Excerpts

A Single Random Triangular Toeplitz Multiplier Ensures Strong Nonsingularity

  • V. Y. Pan, L. Zhao
  • 2014

Supporting GENP with Random Multipliers, Tech. Report TR 2013016

  • V. Y. Pan, G. Qian, X. Yan
  • PhD Program in Comp. Sci., Graduate Center, CUNY,
  • 2013

Report TR 2012009

  • V. Y. Pan, G. Qian, A. Zheng, Randomized Matrix Computations, Tech
  • PhD Program in Comp. Sci., Graduate Center, CUNY,
  • 2012

Similar Papers

Loading similar papers…