Chapter 2.5, Problem 1CP

Use the Jacobi Method to solve the sparse system within six correct decimal places (forward error in the infinity norm) for $n=100$ and $n=\text{1}00000$ . The correct solution is (1,...,1]. Report the number of steps needed and the backward error. The system is $\left[\begin{array}{ccccc}3& -1& & & \\ -1& 3& -1& & \\ & \ddots & \ddots & \ddots & \\ & & -1& 3& -1\\ & & & -1& 3\end{array}\right]\left[\begin{array}{c}{x}_1\\ \begin{array}{c}\\ ⋮\\ \end{array}\\ x_n\end{array}\right]=\left[\begin{array}{c}2\\ \begin{array}{c}1\\ ⋮\\ 1\end{array}\\ 2\end{array}\right]$.