  We consider the problem of finding a low rank symmetric matrix satisfying a
system of linear equations, as appears in phase retrieval. In particular, we
solve the gauge dual formulation, but use a fast approximation of the spectral
computations to achieve a noisy solution estimate. This estimate is then used
as the initialization of an alternating gradient descent scheme over a
nonconvex rank-1 matrix factorization formulation. Numerical results on small
problems show consistent recovery, with very low computational cost.
