Solving systems of linear equations whose matrices are low-rank perturbations of Hermitian matrices, revisited

MINRES-N is a minimal residual algorithm originally developed by the authors for solving systems of linear equations with normal coefficient matrices whose spectra lie on algebraic curves of low degree. In a previous publication, the authors showed that a variant of MINRES-N called MINRES-N2 is applicable to nonnormal matrices $A$ for which
$$ \mathrm{rank}\,(A-A^*)=1. $$
This fact is extended to nonnormal matrices $A$ such that
$$ \mathrm{rank}\,(A-A^*)=k, \qquad k\ge1. $$