Example 2.  Use Jacobi iteration to attempt solving the linear system  [Graphics:Images/GaussSeidelMod_gr_106.gif].
Try 10 iterations.  
Observe that something is not working.  In example 5 we will check to see if this matrix is diagonally dominant.   

Solution 2.

Enter the matrix A, vector B and starting vector P.

[Graphics:../Images/GaussSeidelMod_gr_107.gif]



[Graphics:../Images/GaussSeidelMod_gr_108.gif]

[Graphics:../Images/GaussSeidelMod_gr_109.gif]

Use 10 iterations.

[Graphics:../Images/GaussSeidelMod_gr_110.gif]



[Graphics:../Images/GaussSeidelMod_gr_111.gif]
[Graphics:../Images/GaussSeidelMod_gr_112.gif]
[Graphics:../Images/GaussSeidelMod_gr_113.gif]
[Graphics:../Images/GaussSeidelMod_gr_114.gif]
[Graphics:../Images/GaussSeidelMod_gr_115.gif]
[Graphics:../Images/GaussSeidelMod_gr_116.gif]
[Graphics:../Images/GaussSeidelMod_gr_117.gif]
[Graphics:../Images/GaussSeidelMod_gr_118.gif]
[Graphics:../Images/GaussSeidelMod_gr_119.gif]
[Graphics:../Images/GaussSeidelMod_gr_120.gif]
[Graphics:../Images/GaussSeidelMod_gr_121.gif]

Determine if the method has converged.  

[Graphics:../Images/GaussSeidelMod_gr_122.gif]


[Graphics:../Images/GaussSeidelMod_gr_123.gif]

Was a solution found ?  Why ?

[Graphics:../Images/GaussSeidelMod_gr_124.gif]


[Graphics:../Images/GaussSeidelMod_gr_125.gif]

The matrix A is not diagonally dominant !

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004