Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 187-192
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A. A. Abramov; L. F. Yukhno. Principal vectors of a nonlinear finite-dimensional eigenvalue problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 2, pp. 187-192. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a0/
@article{ZVMMF_2016_56_2_a0,
author = {A. A. Abramov and L. F. Yukhno},
title = {Principal vectors of a nonlinear finite-dimensional eigenvalue problem},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {187--192},
year = {2016},
volume = {56},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a0/}
}
TY - JOUR
AU - A. A. Abramov
AU - L. F. Yukhno
TI - Principal vectors of a nonlinear finite-dimensional eigenvalue problem
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 2016
SP - 187
EP - 192
VL - 56
IS - 2
UR - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a0/
LA - ru
ID - ZVMMF_2016_56_2_a0
ER -
%0 Journal Article
%A A. A. Abramov
%A L. F. Yukhno
%T Principal vectors of a nonlinear finite-dimensional eigenvalue problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 187-192
%V 56
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_2_a0/
%G ru
%F ZVMMF_2016_56_2_a0
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.
