Numerical methods for fermions

The following sections are included:

• Taming the fermion determinant: the Φ algorithm

• Taming the fermion determinant: the R algorithm

• The fourth root approximation

• An exact algorithm for the fourth root: rational hybrid Monte Carlo

• Refinements

  • Sexton-Weingarten scheme

  • Hasenbusch method

  • Schwarz alternating method

• Special considerations for overlap fermions

• Monte Carlo methods for fermions

  • Multiboson method

  • Ratio of determinants

• Conjugate gradient and its relatives

  • Even-odd preconditioning

  • The conjugate gradient algorithm

  • Biconjugate gradient

  • Stabilized biconjugate gradient

  • Shifted solvers

  • Computing fermion eigenmodes