Example 3.  Solve the 31 by 31 system  [Graphics:Images/Tri-DiagonalMod_gr_111.gif]  in Example 1 using Mathematica's built in TridiagonalSolve[a,d,c,b] procedure.    Compute the solution using decimal arithmetic and rational arithmetic.  

Solution 3 (a).

[Graphics:../Images/Tri-DiagonalMod_gr_112.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_113.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_114.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_115.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_116.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_117.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_118.gif]


[Graphics:../Images/Tri-DiagonalMod_gr_119.gif]

We can compare this answer with the previous one in Examples 1 and  2.

[Graphics:../Images/Tri-DiagonalMod_gr_120.gif]


[Graphics:../Images/Tri-DiagonalMod_gr_121.gif]
[Graphics:../Images/Tri-DiagonalMod_gr_122.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004