The overlap Dirac operator as a continued fraction

Abstract

We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method and nested conjugate gradient procedures are avoided. We point out that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions.

7 pages, Talk given at the Third International Workshop on Numerical Analysis and Lattice QCD, Edinburgh, June 2003