  We propose an iterative algorithm for solving the Thouless-Anderson-Palmer
(TAP) equations of Ising models with arbitrary rotation invariant (random)
coupling matrices. In the thermodynamic limit, we prove by means of the
dynamical functional method that the proposed algorithm converges when the
so-called de Almeida Thouless (AT) criterion is fulfilled. Moreover, we give
exact analytical expressions for the rate of the convergence.
