A hybrid neural network algorithm which employs superpositions of linear mappings is presented, and its application to the task of learning the end effector positioning of a robot arm is described. The learning and the control of the positioning is accomplished by the network solely through visual input from a pair of cameras. In addition to the learning of the a priori unknown input-output relation from target locations seen by the cameras to corresponding joint angles, the network provides the robot with the ability to perform feedback-guided corrective movements. This allows one to divide the positioning movement into an initial, open-loop controlled positioning and subsequent feedback-guided corrections, a divison which resembles the strategy for fast goal-directed arm movements of humans. For the robot arm which we employed, a PUMA 560, the neural network algorithm achieves a final positioning error of about 1.3 mm, the lower bound given by the finite resolution of the cameras. Because of the feedback loops, the LMS error correction rules for the weights of the network have the form of Hebbian learning rules, except that instead of the product of the pre- and post-synaptic excitation, it is the product of their time derivatives that determines the adjustment.