Geodesic
On one variational smoothing problem
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 9-22

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

We study the variational approach to setting and solving of the function approximating problem by quasipolynomials which are the solutions of the homogeneous autonomous linear difference or differential equations.
Keywords: linear autonomous difference or differential equations, smoothing, prediction, renewal process, fast recurrence algorithms.
Mots-clés : orthogonal projection, filtration 
A. O. Egorshin. On one variational smoothing problem. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2011), pp. 9-22. http://geodesic.mathdoc.fr/item/VUU_2011_4_a1/
@article{VUU_2011_4_a1,
     author = {A. O. Egorshin},
     title = {On one variational smoothing problem},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {9--22},
     year = {2011},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_4_a1/}
}
TY  - JOUR
AU  - A. O. Egorshin
TI  - On one variational smoothing problem
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 9
EP  - 22
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_4_a1/
LA  - ru
ID  - VUU_2011_4_a1
ER  - 
%0 Journal Article
%A A. O. Egorshin
%T On one variational smoothing problem
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 9-22
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2011_4_a1/
%G ru
%F VUU_2011_4_a1

[1] Linnik Yu. V., Metod naimenshikh kvadratov i osnovy teorii obrabotki rezultatov nablyudenii, Fizmatgiz, M., 1961, 349 pp. | MR

[2] Wiener N., Extrapolation, Interpolation, and Smoothing of Stationary Time Series, Technology Press and Wiley, NY, 1949 | MR | Zbl

[3] Kalman R. E., “A new approach to linear filtering and prediction problems”, Trans. ASME J. Basic Eng. Ser. D, 82 (1960), 34–45, (also published as ASME Paper 59-IRD-11)

[4] Li R., Optimalnye otsenki, opredelenie kharakteristik i upravlenie, Nauka, M., 1966, 176 pp.

[5] Kailath T., “Same New Algorithms for Recursive Estimation in Constant Linear System”, IEEE Trans. Inform. Theory, IT-19:6 (1973), 750–760 | DOI | MR | Zbl

[6] Rao R., Lineinye statisticheskie metody i ikh primenenie, Nauka, M., 1968, 548 pp. | MR | Zbl

[7] Levinson N., “The Wiener RMS (root-mean-square) Error Criterion in Filter Design and Prediction”, J. Math. Phys., 25 (1947), 261–278 | DOI | MR

[8] Krein M. G., “Ob integralnykh uravneniyakh, porozhdayuschikh differentsialnye uravneniya 2-go poryadka”, DAN, 97 (1954), 21–24 | MR

[9] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966, 576 pp. | MR

[10] Egorshin A. O., “Ob odnom sposobe otsenki koeffitsientov modeliruyuschikh uravnenii dlya posledovatelnostei”, Sib. zhurn. industr. matem., 3:2(6) (2000), 78–96 | MR | Zbl

[11] Egorshin A. O., “Identifikatsiya statsionarnykh modelei v unitarnom prostranstve”, Avtomatika i telemekhanika, 2004, no. 12, 29–48 | MR | Zbl

[12] Egorshin A. O., “Variatsionnaya diskretizatsiya i identifikatsiya lineinykh statsionarnykh differentsialnykh uravnenii”, Identifikatsiya sistem i zadachi upravleniya, Trudy III Mezhdunar. konf. SICPRO' 04, IPU RAN, Moskva, 2004, 1824–1883

[13] Yegorshin A. O., “Orthogonalization, Factorization, and Identification: As to The Theory of Recursive Equation In Linear Algebra”, Siberian Electronic Mathematical Reports (SEMR), 4 (2007), 482–503 URL: http://semr.math.nsc.ru/v4/p482-503.pdf | MR | Zbl

[14] Glazman I. M, Lyubich Yu. I., Konechnomernyi lineinyi analiz, Nauka, M., 1969, 475 pp. | MR | Zbl