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Gaze tracking has been suggested as an alternative to traditional computer pointing mechanisms. However, the accuracy limitations of gaze estimation algorithms and the fatigue imposed on users when overloading the visual perceptual channel with a motor control task have prevented the widespread adoption of gaze as a pointing modality. Rather than using gaze as a complete pointing mechanism, this study investigates the usage of gaze to complement traditional keyboard/mouse cursor positioning methods during standard human-computer interaction (HCI). With this approach, bringing the mouse/keyboard cursor to a target still requires a manual action, but the time and effort involved are substantially reduced in terms of mouse movement amplitude incurred or number of keystrokes pressed. This is accomplished by the cursor warping from its original position on the screen to the estimated point of regard of the user on the screen as estimated by video-oculography gaze tracking when a keystroke or mouse movement event is detected. The user adjusts the final fine-grained positioning of the cursor manually. The results of the user study carried out here on the effects of cursor warping in common computer input operations that involve cursor repositioning when using one or several monitors as well as on its learning dynamics over time show that cursor warping can speed up and/or reduce the physical effort required to complete tasks such as mouse/trackpad target acquisition, keyboard text cursor positioning, mouse/keyboard based text selection, and drag and drop operations.