Geodesic
Computation of eigenvalues of perturbed discrete semibounded operators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1265-1272 
S. I. Kadchenko; I. I. Kinzina. Computation of eigenvalues of perturbed discrete semibounded operators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1265-1272. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

To compute the eigenvalues of a perturbed discrete semibounded operator, systems are obtained for the first time in which the number of equations is equal to the multiplicity of the corresponding eigenvalues of the unperturbed operator.

[1] Sadovnichii V. A., Dubrovskii V. V., “Zamechanie ob odnom novom metode vychisleniya sobstvennykh znachenii i sobstvennykh funktsii diskretnykh operatorov”, Tr. seminara im. I. G. Petrovskogo, 17, MGU, M., 1994, 244–248 | MR

[2] Sadovnichii V. A., Podolskii V. E., “O vychislenii pervykh sobstvennykh znachenii operatora Shturma–Liuvillya”, Dokl. RAN, 346:2 (1996), 162–164 | MR

[3] Dorodnitsyn A. A., “Asimptoticheskie zakony raspredeleniya sobstvennykh znachenii dlya nekotorykh vidov differentsialnykh uravnenii vtorogo poryadka”, Uspekhi matem. nauk, 7:6 (1952), 3–96

[4] Dikii L. A., “Novyi sposob priblizhennogo vychisleniya sobstvennykh chisel zadachi Shturma–Liuvillya”, Dokl. AN SSSR, 116:1 (1957), 12–14 | MR

[5] Dikii L. A., “Formuly dlya differentsialnykh operatorov Shturma–Liuvillya”, Uspekhi matem. nauk, 13:3 (1958), 111–143 | MR

[6] Shkarin S. A., “O sposobe Gelfanda–Dikogo vychisleniya pervykh sobstvennykh chisel operatora Shturma–Liuvillya”, Vestn. MGU. Ser. 1. Matem., mekhan., 1996, no. 1, 39–44 | MR

[7] Kadchenko S. I., Novyi metod vychisleniya sobstvennykh chisel vozmuschennykh samosopryazhennykh operatorov, Dis. $\dots$ dokt. fiz.-matem. nauk, MaGU, Magnitogorsk, 2004

[8] Sadovnichii V. A., Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., “Vychislenie pervykh sobstvennykh chisel kraevoi zadachi gidrodinamicheskoi ustoichivosti techeniya mezhdu parallelnymi ploskostyami pri malykh chislakh Reinoldsa”, Dokl. RAN, 335:5 (1997), 600–604 | MR

[9] Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A., “Novyi metod priblizhennogo vychisleniya pervykh sobstvennykh chisel spektralnoi zadachi Orra–Zommerfelda”, Dokl. RAN, 378:4 (2001), 443–446 | MR | Zbl

[10] Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A., “Novyi metod priblizhennogo vychisleniya pervykh sobstvennykh chisel spektralnoi zadachi gidrodinamicheskoi ustoichivosti techeniya Puazeilya v krugloi trube”, Dokl. RAN, 380:2 (2001), 160–163 | MR

[11] Sadovnichii V. A., Teoriya operatorov, Vyssh. shkola, M., 1999