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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 4, Pages 595–600 (Mi zvmmf1)  
This article is cited in 3 scientific papers (total in 3 papers)

Low-rank perturbations of symmetric matrices and their condensed forms under unitary congruences

M. Ghasemi Kamalvanda, Kh. D. Ikramovb

a University of Lorestan, Khorramabad, Islamic Republic of Iran
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
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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.
Key words: normal matrices, onjugate-normal matrices, unitary similarity transformations, unitary congruence transformations, Krylov subspacesm, complex symmetric matrices.
Received: 12.08.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 4, Pages 573–578
DOI: https://doi.org/10.1134/S0965542509040010
Bibliographic databases:
Document Type: Article
UDC: 519.614
Language: Russian
Citation: M. Ghasemi Kamalvand, Kh. D. Ikramov, “Low-rank perturbations of symmetric matrices and their condensed forms under unitary congruences”, Zh. Vychisl. Mat. Mat. Fiz., 49:4 (2009), 595–600; Comput. Math. Math. Phys., 49:4 (2009), 573–578
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v49/i4/p595
    • This publication is cited in the following 3 articles:
    1. Kh. D. Ikramov, “Involutions and Coninvolutions”, Numer. Analys. Appl., 16:4 (2023), 317  crossref
    2. Kamalvand M.G. Farazmandnia B. Aliyari M., “A Method For Solving of Linear System With Normal Coefficient Matrices”, J. Korean Soc. Ind. Appl. Math., 24:3 (2020), 305–320  crossref  isi
    3. Kh. D. Ikramov, “Improved bounds for the recursion width in congruent type methods for solving systems of linear equations”, J. Math. Sci. (N. Y.), 165:5 (2010), 515–520  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:73
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