  In this paper we have considered a finite unitary matrix group with exact
elements being unknown and only approximate elements available. Such a group
becomes inconsistent with its own multiplication table. We found simple
correction formula for such group. When applied iteratively this formula gives
fast convergence of the group elements and allows to perform the group
reconstruction. Next we considered small unitary rotation of entire group which
makes the group consistent with a set of additional conditions. For example, we
might demand that group elements act on certain set of vectors in a predefined
manner. Again, iterative procedure based on this correction shows fast
convergence. All algorithms developed in this paper were implemented in a
Python library which is available as open source software.
