Identification and Discretization of Linear Differential Equations with Constant Coefficients

被引：0

作者：

Egorshin A.O. ^{[1
,2
]}

机构：

[1] Sobolev Institute of Mathematics SB RAS, 4, pr. Akad. Koptyuga, Novosibirsk

[2] Novosibirsk State University, 2, ul. Pirogova, Novosibirsk

来源：

Journal of Mathematical Sciences | 2016年 / 213卷 / 6期

关键词：

Variational Problem; Fundamental Solution; Characteristic Polynomial; Matrix Versus; Principal Mode;

D O I：

10.1007/s10958-016-2746-9

中图分类号：

学科分类号：

摘要：

We consider the variational problem of approximation and identification of finite sequences. Using the identification problem, we study discretization of the corresponding differential equations. We obtain necessary and sufficient conditions for the uniqueness of discretization and identification problems. Under these conditions, the proposed variational discretization and the known analytic discretization lead to the same result. Bibliography: 14 titles. © 2016, Springer Science+Business Media New York.

引用

页码：844 / 856

页数：12

共 11 条

[1]

Egorshin, “On linear differential equation discretization” [in Russian], Bull. South Ural State Univ., Ser. Math. Model. [in Russian], 40, 14, pp. 59-88, (2012)

[2]

Egorshin, “On one variational smoothing problem” [in Russian], Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki, 4, pp. 9-22, (2011)

[3]

Egorshin, “Problem of the piecewise-linear dynamical approximation” [in Russian], Vestn. Udmurt. Univ. Mat. Mekh. Komp’yut. Nauki, 4, pp. 30-45, (2012)

[4]

Egorshin, “Least square method and fast algorithms of identification and filtration (VI method” [in Russian], Avtometriya, 1, pp. 30-42, (1988)

[5]

English transl., (1961)

[6]

Egorshin, “On one estimation method of modeling equation coefficients for sequences” [in Russian], Sib. Zh. Ind. Mat, 2, pp. 78-96, (2000)

[7]

Egorshin, “Numerical closed methods of linear objects identification” [in Russian], Optimal and Self-Adjusting Systems pp. 40–53, Novosibirsk, (1971)

[8]

Osborne M.R., Smyth G.K., A modified Prony algorithm for fitting functions defined by difference equations, SIAM J. Sci. Stat. Comput., 12, 2, pp. 362-382, (1991)

[9]

Aoki M., Yue P.C., On a priori error estimates of some identification methods, IEEE Trans. Autom. Control, 15, 5, pp. 541-548, (1970)

[10]

Gantmacher F.R., The Theory of Matrices [in Russian], Nauka, Moscow, 1966, (1998)

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