I have to convert $Ax=b$ to the form $x=Bx+b$, so $\|B\|_2 < 1$. I'm having serious trouble with picking/creating the matrix $B$ and it's making me nuts. Can someone give me an example or a hint?
The matrix $A \ (m=n=70)$ I'm working with is:
\begin{pmatrix} 2 & 1 & 0 & ... & 0 \\ 1 & 2 & 1 & ... & 0 \\ 0 & 1 & 2 & ... & 0 \\ ... & ... & ... & ...& ...& \\ 0 & ... & 1 & 2 & 1 \\ 0 & ... & 0 & 1 & 2 \end{pmatrix}
the matrix b is:
\begin{pmatrix} 1 \\ 0 \\ ... \\ 0 \\ -1 \end{pmatrix}
x is:
\begin{pmatrix} x_1 \\ x_2 \\ ... \\ x_{70} \end{pmatrix}