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 for a plurality of control points defined on the part; acquiring in an initial coordinate system of the machine actual measurements for the plurality of control points; computing an error between the actual measurements and the theoretical measurements, the error indicative of a mis-positioning of the part in the initial coordinate system; and if 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 thereof to compensate the error, and applying the transformation to the initial coordinate system; otherwise, generating a machining program for manufacturing the part accordingly.