Part $1-$ Jacobi Iteration Method

Recall in the Jacobi method to solve the linear system $Ax=b,$ denote $D$ the diagonal part of $A,$ then the iteration

formula is

$x_{k+1}=x_k+D^{-1}(b-A{x}_k)$

You will implement the Jacobi method based on this form.

You should use the stop criteria as follows: stop the iteration when the latest iterates $x_{k+1}$ and $x_k$ satisfy

$|||||*|{|}_{}||x|{|}_{}=ma{x}_{1}in|x_i|\frac{||x_{k+1}-x_k|{|}_{}}{||x_{k+1}|{|}_{}+\text{e}\text{p}\text{s}}$

with a given error tolerance $|,or$ when the maximal number $of$ iteration $is$ reached. Here, $is$ the machine epsilon,$||$

and $itis$ used $to$ avoid possible division $by0$ when the relative error $is$ computed. The quantity $||*|{|}_{}$ represents the

infinity norm $of$ a vector, which $is$ defined $as||x|{|}_{}=ma{x}_{1}in|x_i|.$ You can use the following MATLAB built$-in$ function