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Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas

The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation efficiency with several orders without loosing accuracy. As an example, we apply the algorithm to study the three-dimensional interacting electron gas under the renormalized-ring-diagram approximation where the Green's function needs to be self-consistently solved. We present the results for the chemical potential, compressibility, free energy, entropy, and specific heat of the system. The ground-state energy obtained by the present calculation is compared with the existing results of Monte Carlo simulation and random-phase approximation.