1. A method for positioning error compensation during manufacturing of a complex-shaped gas turbine engine part with a machine, the method comprising: retrieving theoretical measurements of a plurality of control points defined on the part; acquiring, in an initial coordinate system of the machine, actual measurements of the plurality of control points defined on the part; computing an error between the actual measurements of the part and the theoretical measurements of the part, the error indicative of a mis-positioning of the part in the initial coordinate system; when the error is beyond a predetermined tolerance, computing a transformation matrix representative of at least one transformation to be applied to the initial coordinate system for adjusting at least one of a position and an orientation of the initial coordinate system to compensate the error, and applying the transformation matrix to the initial coordinate system to obtain a transformed coordinate system; and generating a machining program for manufacturing the part based on the transformed coordinate system.