  We analyze the Guruswami--Sudan list decoding algorithm for Reed--Solomon
codes over the complex field for sparse recovery in Compressed Sensing. We
propose methods of stabilizing both the interpolation and the root-finding
steps against numerical instabilities, where the latter is the most sensitive.
For this purpose, we modify the Roth--Ruckenstein algorithm and propose a
method to refine its result using Newton's method. The overall decoding
performance is then further improved using Generalized Minimum Distance
decoding based on intrinsic soft information. This method also allows to obtain
a unique solution of the recovery problem. The approach is numerically
evaluated and shown to improve upon recently proposed decoding techniques.
