The speed of automatic optimization procedures used in surface structure determination by low-energy electron diffraction can be greatly enhanced by the use of linear approximations in the calculation of scattering amplitudes. It is shown how linear approximations can be used in the calculation of derivatives of intensities which are required in the least-squares optimization method. The derivatives with respect to structural and nonstructural parameters are calculated applying a combination of analytic and numerical methods in connection with approximations of the sum over lattice points in the angular momentum representation. Special cases for different structural and nonstructural parameters and simplifications for special geometries are discussed. The computational effort becomes nearly independent of the number of free parameters and enables the analysis of complex surface structures.