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Two Newton-type algorithms using the generalized complex modulus (GCM) criterion for blind equalization and carrier phase recovery are proposed. First the partial Hessian and full Hessian of the real GCM loss function with complex valued arguments are calculated by second-order differential. Then an adaptive pseudo Newton learning algorithm and a full Newton learning algorithm are designed. By using the matrix inversion lemma, both Newton algorithms can be implemented with a computational complexity of O(L2) efficiently, where L is the length of equalizer. Simulation results demonstrate that the two Newton algorithms can achieve automatic carrier phase recovery and exhibit fast convergence rates.