Example 5  Test the matrix A of Examples 2 and 4 to see if A is strictly diagonally dominant.

Solution 5.

We are done !

Aside. We can use Mathematica's Eigensystem subroutine and actually find the spectral radius of    is less than 1.    This is just for fun.

Since the spectral radius is  ,  iteration in Example 4 will not converge.

Aside.  Test the matrix of Example 1.

This is just for fun.

Aside.  Test the matrix of Example 1to see if the spectral radius of    is less than 1.  

Since the spectral radius is  ,  iteration in Example 1 will converge.

(c) John H. Mathews 2004