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arXiv · 1406.5802

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

Victor Y. Pan·Guoliang Qian·Xiaodong Yan
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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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Victor Y. Pan, Guoliang Qian, Xiaodong Yan. 2014-06-23. Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation. https://arxiv.org/abs/1406.5802

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