Balancing matrix factorizations via gradient flow techniques and the singular value decomposition

The authors explore various gradient flows on manifolds which converge exponentially to balanced matrix factorizations, of which the singular value decomposition is the most well known. Such flows are initialized on trivial nonbalanced factorizations. The authors look at flows for the transformation matrix given an initial factorization, as well as flows on matrix factor themselves. More general flows are given that allow the matrix being factorized to be parameter dependent