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We investigate optimal choices for the (outer) iteration method to use when solving linear systems with Neuberger's overlap operator in QCD. Different formulations for this operator give rise to different iterative solvers, which are optimal for the respective formulation. We compare these methods in theory and practice to find the overall optimal one.For the first time, we apply the so-called SUMR method of Jagels and Reichel to the shifted unitary version of Neuberger's operator, and show that this method is in a sense the optimal choice for propagator computations. When solving the ``squared'' equations in a dynamical simulation with two degenerate flavours, it turns out that the CG method should be used.

Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov SubspaceMethods