Example 4.  Solve the 31 by 31 system  [Graphics:Images/Tri-DiagonalMod_gr_136.gif]  in Example 1 using the inverse matrix [Graphics:Images/Tri-DiagonalMod_gr_137.gif] and the computation  [Graphics:Images/Tri-DiagonalMod_gr_138.gif].  

Solution 4 (a).

[Graphics:../Images/Tri-DiagonalMod_gr_139.gif]


[Graphics:../Images/Tri-DiagonalMod_gr_140.gif]
[Graphics:../Images/Tri-DiagonalMod_gr_141.gif]


[Graphics:../Images/Tri-DiagonalMod_gr_142.gif]


[Graphics:../Images/Tri-DiagonalMod_gr_143.gif]
[Graphics:../Images/Tri-DiagonalMod_gr_144.gif]


[Graphics:../Images/Tri-DiagonalMod_gr_145.gif]


[Graphics:../Images/Tri-DiagonalMod_gr_146.gif]
[Graphics:../Images/Tri-DiagonalMod_gr_147.gif]

Compare this answer with the previous ones we obtained in Examples 1-3.

[Graphics:../Images/Tri-DiagonalMod_gr_148.gif]



[Graphics:../Images/Tri-DiagonalMod_gr_149.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_150.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_151.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_152.gif]

Question.  For a tri-diagonal matrix A would you use the  [Graphics:../Images/Tri-DiagonalMod_gr_153.gif]  method of solution ?  Why ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004