Gradient descent of the frame potential

Unit norm tight frames provide Parseval-like decompositions of vectors in terms of possibly nonorthogonal collections of unit norm vectors. One way to prove the existence of unit norm tight frames is to characterize them as the minimizers of a particular energy functional, dubbed the frame potential. We consider this minimization problem from a numerical perspective. In particular, we discuss how by descending the gradient of the frame potential, one, under certain conditions, is guaranteed to produce a sequence of unit norm frames which converge to a unit norm tight frame at a geometric rate. This makes the gradient descent of the frame potential a viable method for numerically constructing unit norm tight frames.