Can someone please explain me how to find convergence rate here?
I’ve found somewhere that the rate of Jacobi convergence is equal to the rate of convergence of a geometric progression with a denominator q = ∥G2∥. Second norm of matrix G here is equal to √18. Is it correct and how to use it then?
$$A = \begin{bmatrix}1&2&-2\\1&1&1\\2&2&1\end{bmatrix}$$
$$G=D^{-1}(-L-U)=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}\cdot \begin{bmatrix}0&-2&2\\-1&0&-1\\-2&-2&0\end{bmatrix}=\begin{bmatrix}0&-2&2\\-1&0&-1\\-2&-2&0\end{bmatrix}$$
Eigenvalue $\lambda_{1}=0$
