Relativistic impulse approximation (RIA) has been widely used in atomic, condensed matter, nuclear, and elementary particle physics. In former treatments of RIA formulation, differential cross sections for Compton scattering processes were factorized into atomic Compton profiles by performing further simplified approximations in the integration. In this study, we develop an ``exact numerical method without using any further simplified approximations or factorization treatments. The validity of the approximations and factorizations used in former RIA treatments can be tested using our approach. Calculations for C, Cu, Ge, and Xe atomic systems are carried out using Dirac-Fock wavefunctions, and comparisons between the proposed approach and former treatments of RIA are performed and discussed in detail. Numerical results indicate that these simplified approximations work reasonably in the Compton peak region, and our results have little difference with the best of the former RIA treatments in the entire energy region. While in regions far from the Compton peak, the RIA results become inaccurate, even when our ``exact numerical treatment is used.
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