随机乘子在高斯和块高斯消元中数值稳定化：证明及低秩近似扩展
Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation
AI总结：
研究证明随机乘子能稳定高斯消元和块高斯消元，同时支持矩阵低秩近似，实验证实分析结果，经验显示循环或Toeplitz乘子效率相近但理论支持较弱。
摘要：
我们证明标准高斯随机乘子在无主元高斯消元和块高斯消元中具有数值稳定化效果。此外，我们证明此类乘子（即使没有常规超采样）预期支持矩阵低秩近似。我们的测试结果与分析一致。经验表明随机循环或Toeplitz乘子效率与高斯乘子相当，但其形式支持更具挑战性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
