Geodesic
An approach for computing eigenvalues of discrete symplectic boundary value problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 54-59.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we give a new method for computing eigenvalues of discrete symplectic boundary-value problems based on the discrete oscillation theory and a modification of the Abramov transfer method for discrete self-adjoint boundary-value problems.
Keywords: discrete symplectic boundary-value problems, oscillation theory, algorithms for computing eigenvalues. 
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Yu. V. Eliseeva. An approach for computing eigenvalues of discrete symplectic boundary value problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 54-59. http://geodesic.mathdoc.fr/item/IVM_2012_7_a6/

[1] Abramov A. A., “Ob otyskanii sobstvennykh funktsii i sobstvennykh znachenii samosopryazhennoi differentsialnoi zadachi”, Zhurn. vychisl. matem. i matem. fiz., 31:6 (1991), 819–831 | MR | Zbl

[2] Abramov A. A., “O vychislenii sobstvennykh znachenii nelineinoi spektralnoi zadachi dlya gamiltonovykh sistem obyknovennykh differentsialnykh uravnenii”, Zhurn. vychisl. matem. i matem. fiz., 41:1 (2001), 29–38 | MR | Zbl

[3] Abramov A. A., “Modifikatsiya odnogo metoda resheniya nelineinoi samosopryazhennoi spektralnoi zadachi dlya gamiltonovykh sistem obyknovennykh differentsialnykh uravnenii”, Zhurn. vychisl. matem. i matem. fiz., 51:1 (2011), 39–43 | MR | Zbl

[4] Došlý O., Kratz W., “Oscillation theorems for symplectic difference systems”, J. Difference Equ. Appl., 13:7 (2007), 585–605 | DOI | MR

[5] Bohner M., Došlý O., “Disconjugacy and transformations for symplectic systems”, Rocky Mountain J. Math., 27:3 (1997), 707–743 | DOI | MR | Zbl

[6] Kratz W., “Discrete oscillation”, J. Difference Equ. Appl., 9:1 (2003), 135–147 | MR | Zbl

[7] Bohner M., Došlý O, Kratz W., “An oscillation theorem for discrete eigenvalue problems”, Rocky Mountain J. Math., 33:4 (2003), 1233–1260 | DOI | MR | Zbl

[8] Došlý O., Kratz W., “Oscillation and spectral theory for symplectic difference systems with separated boundary conditions”, J. Difference Equ. Appl., 16:7 (2010), 831–846 | DOI | MR

[9] Elyseeva J., “Transformations and the number of focal points for conjoined bases of symplectic difference systems”, J. Difference Equ. Appl., 15:11 (2009), 1055–1066 | DOI | MR | Zbl

[10] Eliseeva Yu. V., “Sravnitelnyi indeks dlya reshenii simplekticheskikh sistem raznostnykh uravnenii”, Differents. uravneniya, 45:3 (2009), 431–444 | MR | Zbl

[11] Eliseeva Yu. V., “Teoremy sravneniya dlya simplekticheskikh sistem raznostnykh uravnenii”, Differents. uravneniya, 46:9 (2010), 1329–1342 | MR | Zbl

[12] Gantmakher F. R., Teoriya matrits, Fizmatlit, M., 2004

[13] Golub Dzh., Van Loun Ch., Matrichnye vychisleniya, Mir, M., 1999