Abstract
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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References
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Original Russian Text © M. Ghasemi Kamalvand, Kh.D. Ikramov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 4, pp. 595–600.
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Ghasemi Kamalvand, M., Ikramov, K.D. Low-rank perturbations of symmetric matrices and their condensed forms under unitary congruences. Comput. Math. and Math. Phys. 49, 573–578 (2009). https://doi.org/10.1134/S0965542509040010
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DOI: https://doi.org/10.1134/S0965542509040010