Chapter 2.5, Problem 2CP

Use the Jacobi Method to solve the sparse system within three correct decimal places (forward error in the infinity norm) for $n=100$ . The correct solution is $\left[\text{1, -1, 1, -1,}\mathrm{...}\text{, 1 -1}\right]$ . Report the number of steps needed and the backward error. The system is

$\left[\begin{array}{ccccc}2& 1& & & \\ 1& 2& 1& & \\ & \ddots & \ddots & \ddots & \\ & & 1& 2& 1\\ & & & 1& 2\end{array}\right]\left[\begin{array}{c}{x}_1\\ \begin{array}{c}\\ ⋮\\ \end{array}\\ x_n\end{array}\right]=\left[\begin{array}{c}1\\ \begin{array}{c}0\\ ⋮\\ 0\end{array}\\ -1\end{array}\right]$.