Krylov subspace methods and the sign function: multishifts and deflation in the non-Hermitian case

Abstract

Rational approximations of the matrix sign function lead to multishift methods. For non-Hermitian matrices long recurrences can cause storage problems, which can be circumvented with restarts. Together with deflation we obtain efficient iterative methods, as we show in numerical experiments for the overlap Dirac operator at non-vanishing quark chemical potential for lattices up to size 10^4.