@article{MT_2024_27_4_a5,
author = {V. S. Prokhorov},
title = {Location of the spectrum of a matrix in a domain bounded by a parabola},
journal = {Matemati\v{c}eskie trudy},
pages = {93--114},
year = {2024},
volume = {27},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_2024_27_4_a5/}
}
V. S. Prokhorov. Location of the spectrum of a matrix in a domain bounded by a parabola. Matematičeskie trudy, Tome 27 (2024) no. 4, pp. 93-114. http://geodesic.mathdoc.fr/item/MT_2024_27_4_a5/
[1] Godunov S. K., Modern aspects of linear algebra, Amer. Math. Soc., Providence, RI, 1998 | MR
[2] Daletskii Yu. L., Krein M. G., Stability of solutions to differential equations in Banach spaces, Nauka, M., 1970
[3] Mazko A. G., Localization of the spectrum and stability of dynamical systems, Trudy Inst. Mat., Nats. Akad. Nauk Ukrain, 28, 1999 (in Russian)
[4] Mazko A. G., Matrix equations, spectral problems and stability of dynamic systems, Cambridge Scientific Publishers, Cambridge, 2008 | MR
[5] Bulgak A., Bulgak H., Linear algebra, Selcuk University, Konya, 2001
[6] Bulgak A., Demidenko G., Matveeva I., “On location of the matrix spectrum inside an ellipse”, Selcuk J. Appl. Math., 4:1 (2003), 25–41 | MR
[7] Demidenko G., “On a functional approach to spectral problems of linear algebra”, Selcuk J. Appl. Math., 2:2 (2001), 39–52
[8] Demidenko G. V., Prokhorov V. S., “On location of the matrix spectrum with respect to a parabola”, Mat. trudy, 26:1 (2023), 26-40
[9] Sadkane M., Touhami A., “On modifications to the spectral dichotomy algorithm”, Numer. Funct. Anal. Optim., 34:7 (2013), 791–817 | DOI | MR
[10] Biberdorf E. A., Blinova M. A., Popova N. I., “Modifications of the dichotomy method of a matrix spectrum and their application to stability tasks”, Numer. Anal. Appl., 11:2 (2018), 108–120 | DOI | MR
[11] Biberdorf E. A., “Development of the matrix spectrum dichotomy method”, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy – A Liber Amicorum to Professor Godunov, eds. Demidenko G.V., Romenski E., Toro E., Dumbser M., Springer Nature, Cham, 2020, 37–43 | DOI | MR
[12] Traore S., Dosso M., “Spectral dichotomy methods of a matrix with respect to the general equation of the parabola”, Eur. J. Pure Appl. Math., 15:2 (2022), 681–725 | DOI | MR
[13] Demidenko G. V., Matrix equations, Tutorial, Novosibirsk State University, Novosibirsk, 2009 (in Russian)