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We prove that standard Gaussian random multipliers are expected tonumerically stabilize both Gaussian elimination with no pivoting and blockGaussian elimination. Moreover we prove that such a multiplier (even withoutthe customary oversampling) is expected to support low-rank approximation of amatrix. Our test results are in good accordance with this analysis. Empiricallyrandom circulant or Toeplitz multipliers are as efficient as Gaussian ones, buttheir formal support is more problematic.

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