Geodesic
Computing the sums of Rayleigh–Schrödinger series of perturbed self-adjoint operators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1494-1505 
S. I. Kadchenko. Computing the sums of Rayleigh–Schrödinger series of perturbed self-adjoint operators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 9, pp. 1494-1505. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_9_a4/
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     title = {Computing the sums of {Rayleigh{\textendash}Schr\"odinger} series of perturbed self-adjoint operators},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new method is proposed and validated for computing the sums of number series of discrete operators in perturbation theory with the required accuracy. Its efficiency is demonstrated through numerical computations.

[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] Kadchenko S. I., “Novyi metod vychisleniya sobstvennykh znachenii spektralnoi zadachi Orra–Zommerfelda”, Elektromagnitnye volny i elektronnye sistemy, 5:6 (2000), 4–10 | MR

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

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

[5] Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A., “Novyi metod vychisleniya pervykh sobstvennykh znachenii spektralnoi zadachi gidrodinamicheskoi teorii ustoichivosti techeniya vyazkoi zhidkosti mezhdu dvumya vraschayuschimisya tsilindrami”, Dokl. RAN, 381:3 (2001), 320–324 | MR

[6] Kadchenko S. I., “Novyi metod vychisleniya pervykh sobstvennykh chisel diskretnykh nesamosopryazhennykh operatorov”, Ur-niya Sobolevskogo tipa, Sb. nauchn. rabot, Chelyabinskii gos. un-t, Chelyabinsk, 2002, 42–59 | MR

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

[8] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Gostekhteorizdat, M., 1957

[9] Gantmakher F. R., Teoriya matrits, Nauka, M., 1988 | MR

[10] Lin Tszya-Tszyao, Teoriya gidrodinamicheskoi ustoichivosti, Izd-vo inostr. lit., M., 1958