Pole-based approximation of Fermi-Dirac function

TL;DR

This paper presents two efficient rational approximation methods for the Fermi-Dirac function, leveraging contour integrals and multipole representations, with applications in electronic structure calculations.

Contribution

It introduces two novel approximation techniques with logarithmic complexity, improving computational efficiency for electronic structure calculations.

Findings

Both methods achieve logarithmic computational complexity.

The approaches are suitable for electronic structure calculations.

They provide efficient rational approximations of the Fermi-Dirac function.

Abstract

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.