  We present a novel method to compute the overlap Dirac operator at zero and
nonzero quark chemical potential. To approximate the sign function of large,
sparse matrices, standard methods project the operator on a much smaller Krylov
subspace, on which the matrix function is computed exactly. However, for large
lattices this subspace can still be too large for an efficient calculation of
the sign function. The idea of the new method is to nest Krylov subspace
approximations by making a further projection on an even smaller subspace,
which is then small enough to compute the sign function efficiently, and this
without any noticeable loss of numerical accuracy. We demonstrate the
efficiency of the method both on Hermitian and non-Hermitian matrices.
