#power-iteration

Question 1: Single choice

To estimate the spectral norm of $A$ , you run power iteration on $AA^\top$ : draw a random $v$ , compute $u = (AA^\top)^{10} v$ , and report $\sqrt{\lVert AA^\top u \rVert_2 / \lVert u \rVert_2}$ . How does this estimate compare with the true spectral norm $\sigma_{\max}(A)$ ?

It is never larger than $\sigma_{\max}(A)$ 1
It is never smaller than $\sigma_{\max}(A)$ 2
It can be either larger or smaller, depending on the random start3
It equals $\sigma_{\max}(A)$ exactly after 10 steps4

Timed test