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

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