  Iterative phase retrieval algorithms typically employ projections onto
constraint subspaces to recover the unknown phases in the Fourier transform of
an image, or, in the case of x-ray crystallography, the electron density of a
molecule. For a general class of algorithms, where the basic iteration is
specified by the difference map, solutions are associated with fixed points of
the map, the attractive character of which determines the effectiveness of the
algorithm. The behavior of the difference map near fixed points is controlled
by the relative orientation of the tangent spaces of the two constraint
subspaces employed by the map. Since the dimensionalities involved are always
large in practical applications, it is appropriate to use random matrix theory
ideas to analyze the average-case convergence at fixed points. Optimal values
of the gamma parameters of the difference map are found which differ somewhat
from the values previously obtained on the assumption of orthogonal tangent
spaces.
