Geodesic
Iterative algorithm for calculation of spectral parameters of a quadratic bunch of operators in the Hilbert space
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 1, pp. 79-93 
V. I. Tarakanov; A. O. Dubovik. Iterative algorithm for calculation of spectral parameters of a quadratic bunch of operators in the Hilbert space. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 1, pp. 79-93. http://geodesic.mathdoc.fr/item/SJVM_2015_18_1_a6/
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     title = {Iterative algorithm for calculation of spectral parameters of a~quadratic bunch of operators in the {Hilbert} space},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.

[1] Tarakanov V. I., Uravneniya s kompaktnymi operatorami v gilbertovom prostranstve i iteratsionnye algoritmy ikh resheniya, Izd-vo Tomskogo politekhnicheskogo universiteta, Tomsk, 2007

[2] Tarakanov V. I., Nesterenko M. V., “Iteratsionnyi algoritm issledovaniya i chislennogo resheniya spektralnykh zadach dlya lineinogo puchka kompaktnykh chastichno simmetrichnykh operatorov”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 13:3 (2010), 343–359 | Zbl

[3] Tarakanov V. I., Lysenkova S. A., “Iteratsionnye algoritmy opredeleniya ustoichivosti kolebanii pri nalichii dempfirovaniya”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 15:1 (2012), 101–117 | Zbl

[4] Tarakanov V. I., Nesterenko M. V., “Iterative algorithm of investigation and numerical solving spectral problems for a linear bunch of compact, partially symmetrical operators”, Numerical Analysis and Application, 3:3 (2010), 279–293 | DOI

[5] Tarakanov V. I., Lysenkova S. A., “Iterative Algorithm of Determining the Stability of an Equation of Oscillations with Damping”, Numerical Analysis and Application, 5:1 (2012), 84–98 | DOI | Zbl

[6] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR

[7] Vasileva A. B., Tikhonov N. A., Integralnye uravneniya, Izd-vo MGU, M., 1989 | Zbl

[8] Feodosev V. I., “O kolebaniyakh i ustoichivosti truby pri protekanii cherez nee zhidkosti”, Inzh. sbornik, 10 (1951), 169–178

[9] Sadovnichii V. A., Teoriya operatorov, Izd-vo MGU, M., 1986 | MR

[10] Parlett B., Simmetrichnaya problema sobstvennykh znachenii, Mir, M., 1983 | MR | Zbl

[11] Bai Z., Su Y., “SOAR: A second-order Arnoldi method for the solution of the quadratic eigenvalue problem”, Siam J. Matrix. Anal. Appl., 26:3 (2005), 640–659 | DOI | MR | Zbl

[12] Arnoldi W. E., “The principle of minimized iterations in the solution of the matrix eigenvalue problem”, Quart. Appl. Math., 9 (1951), 17–29 | MR | Zbl

[13] Krylov A. N., “O chislennom reshenii uravneniya, kotorym v tekhnicheskikh voprosakh opredelyayutsya chastoty malykh kolebanii materialnykh sistem”, Izvestiya Akademii nauk SSSR. VII seriya. Otdelenie matematicheskikh i estestvennykh nauk, 1931, no. 4, 491–539 | Zbl

[14] Faddeev D. K., Faddeeva V. N., Vychislitelnye metody lineinoi algebry, Fizmatgiz, M.–L., 1969 | MR

[15] Lanczos C., “An Iteration method for the solution of the eigenvalue problem of linear differential and integral operators”, J. Res. Natl. Bur. Standards, 45:4 (1950), 255–282 | DOI | MR