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In this paper, we develop an algorithm (hereby referred to as the S-function generator: SFG) for the automatic generation of dynamic S-function blocks which can be used for geometrical error compensation of precision machines. The function block is composed of neural network approximations of the geometrical errors of the machines which will serve as the basis for error compensation. It is generated automatically based on only raw calibration data obtained from a laser interferometer and simple user specifications in terms of approximation accuracy requirements. No coding is necessary on the part of the user. This tremendously simplifies the use of the functional error compensation approach which has clear advantages over a traditional look-up table approach. The SFG has been applied to the compensation of two XY tables and the evaluation tests show that the overall geometrical errors can be significantly reduced. [Copyright &y& Elsevier]