概率估计秩1交叉逼近精度
Probabilistic estimation of the rank 1 cross approximation accuracy
AI总结：
本文研究了在低秩矩阵逼近和最大元素搜索中，maxvol算法的概率收敛性，证明了在一定随机性和适当起始列选择下，算法在几步内能收敛到接近最大元素的元素，并展示了在更严格的误差矩阵限制下无需对起始列进行限制。
摘要：
在低秩矩阵逼近和最大元素搜索的构建中，使用maxvol算法是有效的。然而，即使在秩1逼近的情况下，该算法也不总是收敛到最大矩阵元素，不清楚能有多频繁地找到接近最大元素的元素。本文表明，当矩阵具有一定程度的随机性和适当选择起始列时，算法以高概率在几步内收敛到一个元素，其模与最大元素相差很小。此外，还证明在更严格的误差矩阵限制下，无需对起始列进行限制。
英文摘要：
In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the algorithm does not always converge to the maximum matrix element, and it is unclear how often close to the maximum element can be found. In this article it is shown that with a certain degree of randomness in the matrix and proper selection of the starting column, the algorithm with high probability in a few steps converges to an element, which module differs little from the maximum. It is also shown that with more severe restrictions on the error matrix no restrictions on the starting column need to be introduced.
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。
