We derive lower and upper bounds for the distance between a frame and the set of equal-norm Parseval frames.
The lower bound results from variational inequalities. The upper bound is obtained with a technique that uses
a family of ordinary differential equations for Parseval frames which can be shown to converge to an equal-norm
Parseval frame, if the number of vectors in a frame and the dimension of the Hilbert space they span are relatively
prime, and if the initial frame consists of vectors having sufficiently nearly equal norms.