large matrix inversion
I think Matlab code probably uses sparse-matrix techniques that you will find
in the "Numerical Recipes" books. So I am not certain you will gain any better
accuracy in the computation itself from writing your own program.
I am sure there will be some overhead in this computation by running Matlab
instead of running your own program from a command line, for instance.
I would suggest that you try Matlab, or even the linux clone Octave
and see what the computation time really is.
Best regards,
v_c