This article is cited in 3 papers

Principal vectors of a nonlinear finite-dimensional eigenvalue problem

A. A. Abramov^ab, L. F. Yukhno<sup>cd

a</sup> 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

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.

UDC: 519.614

Received: 09.07.2015

DOI: 10.7868/S0044466916020034

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:2, 185–190

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