Improved Fermi operator expansion methods for fast electronic structure calculations

Several algorithms were considered to accelerate the Fermi operator expansion (FOE) method. Novel fast summation methods were used to evaluate a matrix polynomial or Chebyshev matrix polynomial with matrix multiplications totalling roughly twice the square root of the degree of polynomial. Following this, six different representations of the Fermi operators were compared to assess the smallest possible degree of polynomial expansion for a given target precision. Results were analyzed in detail.