Abstract
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.
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