Minimax rational approximation of the Fermi-Dirac distribution.
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ-1)) poles to achieve an error tolerance ϵ at temperature β-1over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. This is particularly beneficial when Δ ≫ Δocc, such as in electronic structure calculations that use a large basis set.
Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
Jonathan E
JE
Moussa