Geodesic
An extension of the Krylov method for calculating the coefficients of the minimal polynomial
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 691-700 
K. O. Vidyaeva; S. M. Ermakov. An extension of the Krylov method for calculating the coefficients of the minimal polynomial. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 691-700. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a0/
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     title = {An extension of the {Krylov} method for calculating the coefficients of the minimal polynomial},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The concept of a $k$-minimal polynomial of an operator is introduced, and a method for approximate calculation of the coefficients of this polynomial is proposed. The method uses the calculated values of certain functionals on iterations of the operator. Special features emerging when the algorithm is used in combination with the Monte-Carlo method are discussed, and numerical results are given.

[1] Gantmakher F. R., Teoriya matrits, Izd. 4-e, dop., Nauka, M., 1988 | MR | Zbl

[2] Ermakov S. M., Vidyaeva K. O., “Ob otsenke spektra lineinogo operatora”, SPb.: Vestnik, Ser. 1, 2012, 11–17

[3] Kertiss D., “Metody Monte-Karlo dlya iteratsii lineinykh operatorov”, UMN, 1957, no. 5, 149–174

[4] Uilks S., Matematicheskaya statistika, Nauka, M., 1967 | MR

[5] Ermakov S., “MCQMC Algorithms for some classes of equations”, Monte Carlo and Quasi-Monte Carlo Methods 2006, eds. Keller A., Heinrich S., Niderreitereds H., Springer, Berlin, 2008 | MR

[6] Ermakov S. M., Metod Monte-Karlo v vychislitelnoi matematike. Vvodnyi kurs, Nevskii Dialekt, SPb.; Binom, M., 2009