Example 1 (a).  Find the  A = LU factorization for the matrix  [Graphics:Images/CholeskyMod_gr_52.gif].  Use the Doolittle method.  
Solution 1 (a).

Enter the matrix.

 

[Graphics:../Images/CholeskyMod_gr_55.gif]

Invoke the subroutine Doolittle.  

[Graphics:../Images/CholeskyMod_gr_56.gif]



[Graphics:../Images/CholeskyMod_gr_57.gif]

[Graphics:../Images/CholeskyMod_gr_58.gif]

[Graphics:../Images/CholeskyMod_gr_59.gif]

[Graphics:../Images/CholeskyMod_gr_60.gif]


Verify the factorization.

[Graphics:../Images/CholeskyMod_gr_61.gif]



[Graphics:../Images/CholeskyMod_gr_62.gif]

[Graphics:../Images/CholeskyMod_gr_63.gif]

[Graphics:../Images/CholeskyMod_gr_64.gif]

[Graphics:../Images/CholeskyMod_gr_65.gif]

[Graphics:../Images/CholeskyMod_gr_66.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004