How is the MATLAB LU decomposition so accurate?

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Mircea Susca
Mircea Susca 2018-8-3
Hello,
I wanted to implement my own LU factorization algorithm and I compared it with the output produced by the standard lu function in MATLAB. The results are correct, as the norm of the residual A-L*U has a very small value.
What other principle is applied in the MATLAB implementation of the algorithm as it is a lot more consistent and accurate compared with the basic factorization? I also tried partial, rook and complete pivoting and it's still a few orders of magnitude weaker generally. Is there some iterative refinement applied on the matrices or does the proprietary implementation have access to some extended precision when using the CPU?
I uploaded a plot of the comparison of the two methods.

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