Computational methods for the fermion determinant and the link between overlap and domain wall fermions

Details Computational methods for the fermion determinant and the link between overlap and domain wall fermions Computational methods for the fermion determinant and the link between overlap and domain wall fermions

2004-02-26

arxiv.org/abs/hep-lat/0402035v1

Physics

High Energy Physics

High Energy Physics - Lattice

Talk given at the Third International Workshop on Numerical Analysis and Lattice QCD held in Edinburgh, June-July 2003. 15 pag

Scientific paper

This paper reviews the most popular methods which are used in lattice QCD to compute the determinant of the lattice Dirac operator: Gaussian integral representation and noisy methods. Both of them lead naturally to matrix function problems. We review the most recent development in Krylov subspace evaluation of matrix functions. The second part of the paper reviews the formal relationship and algebraic structure of domain wall and overlap fermions. We review the multigrid algorithm to invert the overlap operator. It is described here as a preconditioned Jacobi iteration where the preconditioner is the Schur complement of a certain block of the truncated overlap matrix.

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