The next iteration results in $$\begin{equation*} \hat{w}(t=2\epsilon) = \hat{W}\hat{w}(t=\epsilon), \end{equation*}$$

resulting in $$\begin{equation*} \hat{w}(t=2\epsilon)= \left(\begin{array}{c} 0.201389\\ 0.319444 \\ 0.055556 \\ 0.423611 \end{array} \right). \end{equation*}$$ Note that the vector $\hat{w}$ is always normalized to $1$.