I see that this is done in the Matlab code. But still I do not agree on computing/storing matrix inverses. You can always solve the corresponding linear system A^-1 * b, which is better than storing A^-1 and multiplying it to b.
See the ```solve()``` method of the decomposition base class of Eigen3.

Also, why did you choose this particular decomposition? See http://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html
Such choices should be documented, explained etc.