Example 4  Use Gauss-Seidel iteration to attempt solving the linear system  [Graphics:Images/GaussSeidelMod_gr_202.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 4.

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

[Graphics:../Images/GaussSeidelMod_gr_203.gif]



[Graphics:../Images/GaussSeidelMod_gr_204.gif]

[Graphics:../Images/GaussSeidelMod_gr_205.gif]

Use 10 iterations.

[Graphics:../Images/GaussSeidelMod_gr_206.gif]



[Graphics:../Images/GaussSeidelMod_gr_207.gif]
[Graphics:../Images/GaussSeidelMod_gr_208.gif]
[Graphics:../Images/GaussSeidelMod_gr_209.gif]
[Graphics:../Images/GaussSeidelMod_gr_210.gif]
[Graphics:../Images/GaussSeidelMod_gr_211.gif]
[Graphics:../Images/GaussSeidelMod_gr_212.gif]
[Graphics:../Images/GaussSeidelMod_gr_213.gif]
[Graphics:../Images/GaussSeidelMod_gr_214.gif]
[Graphics:../Images/GaussSeidelMod_gr_215.gif]
[Graphics:../Images/GaussSeidelMod_gr_216.gif]
[Graphics:../Images/GaussSeidelMod_gr_217.gif]

[Graphics:../Images/GaussSeidelMod_gr_218.gif]

Was a solution found ?  Why ?

[Graphics:../Images/GaussSeidelMod_gr_219.gif]


[Graphics:../Images/GaussSeidelMod_gr_220.gif]

The matrix A is not diagonally dominant !

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004