2019/07/22 by A. S. Mysovsky, Mysovsky, Andrey S.
Computer Science · #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1907.13543
In this paper we have considered a finite unitary matrix group with exact\nelements being unknown and only approximate elements available. Such a group\nbecomes inconsistent with its own multiplication table. We found simple\ncorrection formula for such group. When applied iteratively this formula gives\nfast convergence of the group elements and allows to perform the group\nreconstruction. Next we considered small unitary rotation of entire group which\nmakes the group consistent with a set of additional conditions. For example, we\nmight demand that group elements act on certain set of vectors in a predefined\nmanner. Again, iterative procedure based on this correction shows fast\nconvergence. All algorithms developed in this paper were implemented in a\nPython library which is available as open source software.\n