>> A

A =

     6     3     4     8
     3     6     5     1
     4     5    10     7
     8     1     7    25

>> chol(A)

ans =

   2.449489742783178   1.224744871391589   1.632993161855452   3.265986323710905
                   0   2.121320343559642   1.414213562373095  -1.414213562373096
                   0                   0   2.309401076758503   1.587713240271470
                   0                   0                   0   3.132491021535417

>> generalized_cholesky2(A)

ans =

   2.449489742783178   1.224744871391589   1.632993161855452   3.265986323710905
                   0                   0                   0                   0
                   0                   0   2.708012801545320   0.615457454896663
                   0                   0                   0   3.735578329328064

>>