随机乘子数值稳定高斯消元与块高斯消元：证明及到低秩逼近的推广
数值分析
2014-12-18 v2
摘要
我们证明了标准高斯随机乘子有望数值稳定无选主元的高斯消元法和块高斯消元法。此外，我们证明了此类乘子（即使没有常规的过采样）有望支持矩阵的低秩逼近。我们的测试结果与该分析高度吻合。经验表明，随机循环或 Toeplitz 乘子与高斯乘子效率相当，但其形式化支持更为困难。
引用
@article{arxiv.1406.5802,
title = {Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation},
author = {Victor Y. Pan and Guoliang Qian and Xiaodong Yan},
journal= {arXiv preprint arXiv:1406.5802},
year = {2014}
}
备注
34 pages; 7 figures appeared separately from legends, but in correct order