Appendix C: Notes about the KPM and FOE

• Kernel polynomial method
  • Chebyshev Polynomials
  • Density of states
  • Fermi energy, number of electrons and electronic energy
  • Testing and comparison of the KPM and the FOE
  • Calculation of the moments
• Fermi operator expansion (FOE) method
  • Fermi operator
  • Chebyshev expansion of the Fermi operator
• Computational considerations
  • Bulk of the computation
  • Size scaling considerations
  • Parallel implementation