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 
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/
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     title = {Solving systems of linear equations whose matrices are low-rank perturbations of {Hermitian} matrices, revisited},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a4/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 $$ \mathrm{rank}\,(A-A^*)=k, \qquad k\ge1. $$

[1] M. Dana, A. G. Zykov, Kh. D. Ikramov, “Metod minimalnykh nevyazok dlya spetsialnogo klassa lineinykh sistem s normalnymi matritsami koeffitsientov”, Zh. vychisl. matem. matem. fiz., 45 (2005), 1928–1937 | MR | Zbl

[2] M. Dana, Kh. D. Ikramov, “O reshenii sistem lineinykh uravnenii, matritsy kotorykh yavlyayutsya malorangovymi vozmuscheniyami ermitovykh matrits”, Vestn. MGU. Seriya “Vychisl. matematika i kibernetika”, 2005, no. 1, 15–22 | MR | Zbl