Example 1 (b).  Find the A = LU  factorization for the matrix  .  Use the Crout method.  

Solution 1 (b).

Enter the matrix.

Invoke the subroutine Crout.  

Verify the factorization.

The matrix has been factored it is similar to the Doolittle factorization. But this time the elements on the diagonal of  U  are .  

Aside.  This is different from the Doolittle factorization that we found in part (a).

Remark.  If the LU factorization is used to solve a linear system then a wee bit more computing effort required for the Crout factorization than the Doolittle factorization.  For this reason we prefer the Doolittle method.

(c) John H. Mathews 2004