Geodesic
Low-rank perturbations of symmetric matrices and their condensed forms under unitary congruences
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 595-600

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The method MINRES-CN was earlier proposed by the authors for solving systems of linear equations with conjugate-normal coefficient matrices. It is now shown that this method is also applicable even if the coefficient matrix, albeit not conjugate-normal, is a low-rank perturbation of a symmetric matrix. If the perturbed matrix is still conjugate-normal, then, starting from some iteration step, the recursion underlying MINRES-CN becomes a three-term relation. These results are proved in terms of matrix condensed forms with respect to unitary congruences. 
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     author = {M. Ghasemi Kamalvand and Kh. D. Ikramov},
     title = {Low-rank perturbations of symmetric matrices and their condensed forms under unitary congruences},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a0/}
}
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M. Ghasemi Kamalvand; Kh. D. Ikramov. Low-rank perturbations of symmetric matrices and their condensed forms under unitary congruences. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 595-600. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a0/