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We investigate the Brillouin action in terms of its suitability as a kernelto the overlap procedure, with a view on both heavy and light quark physics. Weuse the diagonal elements of the Kenney-Laub family of iterations for thesparse matrix sign function, since they grow monotonically and facilitatecascaded preconditioning strategies with different rational approximations tothe sign function. We find that the overlap action with the Brillouin kernel issignificantly better localized than the version with the Wilson kernel.

On the suitability of the Brillouin action as a kernel to the overlap procedure