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The use of three simple fixed-point iteration quadratic programming (QP) solvers in input constrained model predictive control (MPC) has been reported (Syaichu-Rohman et al., 2003), that may be seen as gradient projection based methods. They were employed as alternatives to existing algorithms such as active-set method and interior point algorithm. A convergence analysis of those three QP algorithms is the subject of the paper. Two stopping criteria with guaranteed performances are described. While the first is based on an error between an actual and its computed upper bound cost, a primal-dual error cost is the basis for the second stopping criterion. Scaling techniques are also presented for each simple algorithm to help increase its convergence rate. Some results from comparative numerical studies are also given in the examples.