Geodesic
Solving systems of linear equations whose matrices are low-rank perturbations of Hermitian matrices, revisited
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 68-77

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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 $$ \mathrm{rank}\,(A-A^*)=k, \qquad k\ge1. $$ 
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     author = {M. Dana and Kh. D. Ikramov},
     title = {Solving systems of linear equations whose matrices are low-rank perturbations of {Hermitian} matrices, revisited},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {68--77},
     publisher = {mathdoc},
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     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a4/}
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M. Dana; Kh. D. Ikramov. Solving systems of linear equations whose matrices are low-rank perturbations of Hermitian matrices, revisited. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 68-77. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a4/