Geodesic
Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1219-1231 
R. S. Martynov; Yu. M. Nechepurenko. Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1219-1231. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a5/
@article{ZVMMF_2006_46_7_a5,
     author = {R. S. Martynov and Yu. M. Nechepurenko},
     title = {Finding the response matrix to the external action from a~subspace for a~discrete linear stochastic dynamical system},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1219--1231},
     year = {2006},
     volume = {46},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a5/}
}
TY  - JOUR
AU  - R. S. Martynov
AU  - Yu. M. Nechepurenko
TI  - Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1219
EP  - 1231
VL  - 46
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a5/
LA  - ru
ID  - ZVMMF_2006_46_7_a5
ER  - 
%0 Journal Article
%A R. S. Martynov
%A Yu. M. Nechepurenko
%T Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1219-1231
%V 46
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a5/
%G ru
%F ZVMMF_2006_46_7_a5

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

For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented.

[1] Martynov P. C., Nechepurenko Yu. M., “O nakhozhdenii matritsy otklika lineinoi diskretnoi dinamiko-stokhasticheskoi sistemy”, Zh. vychisl. matem. i matem. fiz., 44:5 (2004), 817–826 | MR | Zbl

[2] Bulgakov A. Ya., Godunov S. K., “Krugovaya dikhotomiya matrichnogo spektra”, Sibirskii matem. zhurnal, 29:5 (1988), 59–70 | MR

[3] Godunov S. K., Sovremennye aspekty lineinoi algebry, Nauchn. kniga, Novosibirsk, 1997

[4] Nechepurenko Yu. M., “Otsenka normy matrichnoi eksponenty cherez normu resheniya uravneniya Lyapunova i granitsy khausdorfova mnozhestva”, Zh. vychisl. matem. i matem. fiz., 42:2 (2002), 131–141 | MR | Zbl

[5] Veselic K., “Bounds for exponentially stable semigroups”, Linear Algebra Appl., 358 (2003), 309–333 | DOI | MR | Zbl

[6] Gritsoun A. S., Branstator G., Dymnikov V. P., “Construction of the linear response operator of an atmospheric general circulation model to small external forcing”, Rus. J. Numer. Analys. Math. Modeling., 17:5 (2002), 399–416 | MR | Zbl

[7] Klyatskin V. I., Stokhasticheskie uravneniya glazami fizika, Fizmatlit, M., 2001 | MR | Zbl

[8] Bretherton Ch. S., Widmann M., Dymnikov V. P. et al., “The effective number of spatial degrees of freedom of a timevarying field”, J. Climate, 12 (1999), 1990–2009 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[9] Bagrov H. A., “Ob ekvivalentnom chisle nezavisimykh dannykh”, Tr. Gidrometeotsentra, 44, M., 1969, 3–11