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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 2, Pages 187–192
DOI: https://doi.org/10.7868/S0044466916020034 (Mi zvmmf10335) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Principal vectors of a nonlinear finite-dimensional eigenvalue problem

A. A. Abramovab, L. F. Yukhnocd

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
c Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
d Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow, 115409, Russia
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DOI: https://doi.org/10.7868/S0044466916020034
Abstract: In a finite-dimensional linear space, consider a nonlinear eigenvalue problem analytic with respect to its spectral parameter. The notion of a principal vector for such a problem is examined. For a linear eigenvalue problem, this notion is identical to the conventional definition of principal vectors. It is proved that the maximum number of linearly independent eigenvectors combined with principal (associated) vectors in the corresponding chains is equal to the multiplicity of an eigenvalue. A numerical method for constructing such chains is given.
Key words: nonlinear eigenvalue problem, multiplicity of an eigenvalue, eigenvector, principal vector.
Received: 09.07.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 2, Pages 185–190
DOI: https://doi.org/10.1134/S0965542516020032
Bibliographic databases:
Document Type: Article
UDC: 519.614
Language: Russian
Citation: A. A. Abramov, L. F. Yukhno, “Principal vectors of a nonlinear finite-dimensional eigenvalue problem”, Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016), 187–192; Comput. Math. Math. Phys., 56:2 (2016), 185–190
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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