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In this paper, we study unmanned aerial vehicle (UAV) assisted mobile edge computing (MEC) with the objective to optimize computation offloading with minimum UAV energy consumption. In the considered scenario, a UAV plays the role of an aerial cloudlet to collect and process the computation tasks offloaded by ground users. Given the service requirements of users, we aim to maximize UAV energy efficiency by jointly optimizing the UAV trajectory, the user transmit power, and computation load allocation. The resulting optimization problem corresponds to nonconvex fractional programming, and the Dinkelbach algorithm and the successive convex approximation (SCA) technique are adopted to solve it. Furthermore, we decompose the problem into multiple subproblems for distributed and parallel problem solving. To cope with the case when the knowledge of user mobility is limited, we adopt a spatial distribution estimation technique to predict the location of ground users so that the proposed approach can still be applied. Simulation results demonstrate the effectiveness of the proposed approach for maximizing the energy efficiency of UAV.