$LDL^t$ Factorization Algorithm to find a factorization of the form A For $$
        \begin{pmatrix}
        4 & 2 & 2 \\
        2 & 6 & 2 \\
        2 & 2 & 5 \\
        \end{pmatrix}
$$ I found that $$
        L=\begin{pmatrix}
        1 & 0 & 0 \\
        1/2 & 1 & 0 \\
        1/2 & 1/5 & 1 \\
        \end{pmatrix}
$$ and $$
        D=\begin{pmatrix}
        4 & 0 & 0 \\
        0 & 5 & 0 \\
        0 & 0 & 18/5 \\
        \end{pmatrix}
$$
However, when I calculate $LDL^t$, I always get $$
        \begin{pmatrix}
        4 & 2 & 2 \\
        2 & 6 & 2 \\
        2 & 2 & 24/5 \\
        \end{pmatrix},
$$ which does not equal to Matrix A.
Did I make a mistake? but 24/5 and 5 are pretty close. Can someone please help? Thanks!

Using the algorithm located at this site, you should get:
$$L = \left(
\begin{array}{ccc}
 1 & 0 & 0 \\
 \dfrac{1}{2} & 1 & 0 \\
 \dfrac{1}{2} & \dfrac{1}{5} & 1 \\
\end{array}
\right)$$
$$D = \left(
\begin{array}{ccc}
 4 & 0 & 0 \\
 0 & 5 & 0 \\
 0 & 0 & \dfrac{19}{5} \\
\end{array}
\right)$$
