Random Multipliers Numerically Stabilize Gaussian and Block Gaussian   Elimination: Proofs and an Extension to Low-rank Approximation
  We prove that standard Gaussian random multipliers are expected to numerically stabilize both Gaussian elimination with no pivoting and block Gaussian elimination. Moreover we prove that such a multiplier (even without the customary oversampling) is expected to support low-rank approximation of a matrix. Our test results are in good accordance with this analysis. Empirically random circulant or Toeplitz multipliers are as efficient as Gaussian ones, but their formal support is more problematic. 
Victor Y. Pan, Guoliang Qian, and Xiaodong Yan
math.NA