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Minimax rational approximation of the Fermi-Dirac distribution
1Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
The Journal of Chemical Physics
|November 3, 2016
Summary
Researchers developed a new minimax approximation method to improve rational approximations of the Fermi-Dirac distribution. This method significantly reduces the number of poles needed for accurate electronic structure calculations, especially with large basis sets.
Area of Science:
- Computational Physics
- Quantum Chemistry
- Numerical Analysis
Background:
- Rational approximations of the Fermi-Dirac distribution are crucial for numerical algorithms in electronic structure calculations.
- Existing methods often require a large number of poles for desired accuracy, impacting computational efficiency.
Purpose of the Study:
- To develop a more efficient rational approximation for the Fermi-Dirac distribution.
- To reduce the computational cost of electronic structure calculations by minimizing the number of required poles.
Main Methods:
- Application of minimax approximation techniques.
- Focusing on the occupied energy interval (Δocc) instead of the full energy interval (Δ).
Main Results:
- Reduced the number of poles by a factor of four compared to existing methods.
- Achieved significant benefits when the occupied energy interval is much smaller than the total energy interval (Δ ≫ Δocc).
Conclusions:
- The minimax approximation offers a more efficient approach for Fermi-Dirac distribution approximations.
- This method is particularly advantageous for electronic structure calculations employing large basis sets, leading to faster and more accurate results.
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