Let $F^{*}$ be an approximation of a given $(a \times b)$ matrix $F$ derived by methods that are not randomized. We prove that for a given $F$ and $F^{*}$, $H$ and $T$ can be computed by randomized algorithm such that $(HT)$ is an approximation of $F$ better than $F^{*}$.

翻译：以美元为单位的美元值(a\ times b) 矩阵的近似值,用非随机化的方法得出。 我们证明,对于给定的美元值和给定的美元值,H美元和T美元值可以通过随机化算法计算,因此,(HT) 美元值的近似值比F$值好。