I came across an article that makes me doubt what I have learnt so far.
For example, let us decompose matrix A into L and U (LU factorization)
$A=\left(
\begin{array}{cccc}
5 & 4 & 1 & 1 \\
4 & 5 & 1 & 1 \\
1&1&4&2 \\
1&1&2&4
\end{array}\right)$
The Frobenius norm should be $\lVert A-LU\rVert$. Now, the authors gave different answers when they implement this on MATLAB 2010 and 2012 and also different answers on AMD and Intel processor. Why should we have different answers for a consistent norm?