Example 1.  Use Jacobi iteration to solve the linear system  [Graphics:Images/GaussSeidelMod_gr_30.gif].  
Try 10, 20 and 30 iterations.  

Solution 1.

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

[Graphics:../Images/GaussSeidelMod_gr_31.gif]



[Graphics:../Images/GaussSeidelMod_gr_32.gif]

[Graphics:../Images/GaussSeidelMod_gr_33.gif]

Use 10 iterations.

[Graphics:../Images/GaussSeidelMod_gr_34.gif]



[Graphics:../Images/GaussSeidelMod_gr_35.gif]
[Graphics:../Images/GaussSeidelMod_gr_36.gif]
[Graphics:../Images/GaussSeidelMod_gr_37.gif]
[Graphics:../Images/GaussSeidelMod_gr_38.gif]
[Graphics:../Images/GaussSeidelMod_gr_39.gif]
[Graphics:../Images/GaussSeidelMod_gr_40.gif]
[Graphics:../Images/GaussSeidelMod_gr_41.gif]
[Graphics:../Images/GaussSeidelMod_gr_42.gif]
[Graphics:../Images/GaussSeidelMod_gr_43.gif]
[Graphics:../Images/GaussSeidelMod_gr_44.gif]
[Graphics:../Images/GaussSeidelMod_gr_45.gif]

Determine if the method has converged.  

[Graphics:../Images/GaussSeidelMod_gr_46.gif]


[Graphics:../Images/GaussSeidelMod_gr_47.gif]

Use 20 iterations.

[Graphics:../Images/GaussSeidelMod_gr_48.gif]



[Graphics:../Images/GaussSeidelMod_gr_49.gif]
[Graphics:../Images/GaussSeidelMod_gr_50.gif]
[Graphics:../Images/GaussSeidelMod_gr_51.gif]
[Graphics:../Images/GaussSeidelMod_gr_52.gif]
[Graphics:../Images/GaussSeidelMod_gr_53.gif]
[Graphics:../Images/GaussSeidelMod_gr_54.gif]
[Graphics:../Images/GaussSeidelMod_gr_55.gif]
[Graphics:../Images/GaussSeidelMod_gr_56.gif]
[Graphics:../Images/GaussSeidelMod_gr_57.gif]
[Graphics:../Images/GaussSeidelMod_gr_58.gif]
[Graphics:../Images/GaussSeidelMod_gr_59.gif]
[Graphics:../Images/GaussSeidelMod_gr_60.gif]
[Graphics:../Images/GaussSeidelMod_gr_61.gif]
[Graphics:../Images/GaussSeidelMod_gr_62.gif]
[Graphics:../Images/GaussSeidelMod_gr_63.gif]
[Graphics:../Images/GaussSeidelMod_gr_64.gif]
[Graphics:../Images/GaussSeidelMod_gr_65.gif]
[Graphics:../Images/GaussSeidelMod_gr_66.gif]
[Graphics:../Images/GaussSeidelMod_gr_67.gif]
[Graphics:../Images/GaussSeidelMod_gr_68.gif]
[Graphics:../Images/GaussSeidelMod_gr_69.gif]

Determine if the method has converged.  

[Graphics:../Images/GaussSeidelMod_gr_70.gif]


[Graphics:../Images/GaussSeidelMod_gr_71.gif]

Use 30 iterations.

[Graphics:../Images/GaussSeidelMod_gr_72.gif]



[Graphics:../Images/GaussSeidelMod_gr_73.gif]
[Graphics:../Images/GaussSeidelMod_gr_74.gif]
[Graphics:../Images/GaussSeidelMod_gr_75.gif]
[Graphics:../Images/GaussSeidelMod_gr_76.gif]
[Graphics:../Images/GaussSeidelMod_gr_77.gif]
[Graphics:../Images/GaussSeidelMod_gr_78.gif]
[Graphics:../Images/GaussSeidelMod_gr_79.gif]
[Graphics:../Images/GaussSeidelMod_gr_80.gif]
[Graphics:../Images/GaussSeidelMod_gr_81.gif]
[Graphics:../Images/GaussSeidelMod_gr_82.gif]
[Graphics:../Images/GaussSeidelMod_gr_83.gif]
[Graphics:../Images/GaussSeidelMod_gr_84.gif]
[Graphics:../Images/GaussSeidelMod_gr_85.gif]
[Graphics:../Images/GaussSeidelMod_gr_86.gif]
[Graphics:../Images/GaussSeidelMod_gr_87.gif]
[Graphics:../Images/GaussSeidelMod_gr_88.gif]
[Graphics:../Images/GaussSeidelMod_gr_89.gif]
[Graphics:../Images/GaussSeidelMod_gr_90.gif]
[Graphics:../Images/GaussSeidelMod_gr_91.gif]
[Graphics:../Images/GaussSeidelMod_gr_92.gif]
[Graphics:../Images/GaussSeidelMod_gr_93.gif]
[Graphics:../Images/GaussSeidelMod_gr_94.gif]
[Graphics:../Images/GaussSeidelMod_gr_95.gif]
[Graphics:../Images/GaussSeidelMod_gr_96.gif]
[Graphics:../Images/GaussSeidelMod_gr_97.gif]
[Graphics:../Images/GaussSeidelMod_gr_98.gif]
[Graphics:../Images/GaussSeidelMod_gr_99.gif]
[Graphics:../Images/GaussSeidelMod_gr_100.gif]
[Graphics:../Images/GaussSeidelMod_gr_101.gif]
[Graphics:../Images/GaussSeidelMod_gr_102.gif]
[Graphics:../Images/GaussSeidelMod_gr_103.gif]

Determine if the method has converged.  

[Graphics:../Images/GaussSeidelMod_gr_104.gif]


[Graphics:../Images/GaussSeidelMod_gr_105.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004