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 rational arithmetic.  

Solution 3 (b).

[Graphics:../Images/Tri-DiagonalMod_gr_123.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_124.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_125.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_126.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_127.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_128.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_129.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_130.gif]

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

[Graphics:../Images/Tri-DiagonalMod_gr_131.gif]



[Graphics:../Images/Tri-DiagonalMod_gr_132.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_133.gif]

[Graphics:../Images/Tri-DiagonalMod_gr_134.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004