Geodesic
Application of the least square method to the solving linear differential-algebraic equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 81-95 
V. F. Chistyakov; E. V. Chistyakova. Application of the least square method to the solving linear differential-algebraic equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 81-95. http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a8/
@article{SJVM_2013_16_1_a8,
     author = {V. F. Chistyakov and E. V. Chistyakova},
     title = {Application of the least square method to the solving linear differential-algebraic equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {81--95},
     year = {2013},
     volume = {16},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a8/}
}
TY  - JOUR
AU  - V. F. Chistyakov
AU  - E. V. Chistyakova
TI  - Application of the least square method to the solving linear differential-algebraic equations
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2013
SP  - 81
EP  - 95
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a8/
LA  - ru
ID  - SJVM_2013_16_1_a8
ER  - 
%0 Journal Article
%A V. F. Chistyakov
%A E. V. Chistyakova
%T Application of the least square method to the solving linear differential-algebraic equations
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2013
%P 81-95
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a8/
%G ru
%F SJVM_2013_16_1_a8

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

We consider application of the least square method to the numerical solution of a linear system of ordinary differential equations (ODEs) with an identically singular matrix multiplied a higher derivative by the desired vector-function. We discuss the behavior of the gradient method for minimizing the functional of the residual square in the Sobolev space and some other issues. The results of the numerical experiments are given.

[1] Brenan K. E., Campbell S. L., Petzold L. R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Classics in Applied Mathematics, 14, SIAM, Philadelphia, 1996 | MR | Zbl

[2] Boyarintsev Yu. E., Chistyakov V. F., Algebro-differentsialnye sistemy. Metody resheniya i issledovaniya, Nauka, Novosibirsk, 1998 | MR | Zbl

[3] Chistyakov V. F., “K metodam resheniya singulyarnykh lineinykh sistem obyknovennykh differentsialnykh uravnenii”, Vyrozhdennye sistemy obyknovennykh differentsialnykh uravnenii, Nauka, Novosibirsk, 1982, 37–66 | MR

[4] Bulatov M. V., Chistyakov V. F., “Reshenie algebro-differentsialnykh sistem metodom naimenshikh kvadratov”, Tr. XI Mezhdunar. Baikalskoi shkoly-seminara (Irkutsk, Baikal, 5–12 iyulya 1998 g.), v. 4, 72–75

[5] Gorbunov V. K., “Metod normalnoi splain-kollokatsii”, ZhVMiMF, 29:2 (1989), 212–224 | MR | Zbl

[6] Gorbunov V. K., Petrischev V. V., “Razvitie metoda normalnoi splain-kollokatsii dlya lineinykh differentsialnykh uravnenii”, ZhVMiMF, 43:8 (2003), 1150–1159 | MR | Zbl

[7] Gorbunov V. K., Lutoshkin I. V., “The parametrization method in optimal control problems and differential algebraic equations”, J. Comput. Appl. Mathem., 185:2 (2006), 377–390 | DOI | MR | Zbl

[8] Gorbunov V. K., Sviridov V. Yu., “The method of normal splines for linear DAEs on the number semi-axis”, Appl. Numer. Math., 59:3–4 (2009), 656–670 | DOI | MR | Zbl

[9] Bulatov M. V., Gorbunov V. K., Martynenko Yu. V., Nguen Din Kong, “Variatsionnye podkhody k chislennomu resheniyu differentsialno-algebraicheskikh uravnenii”, Vychislitelnye tekhnologii, 15:5 (2010), 3–13 | Zbl

[10] Gantmakher F. R., Teoriya matrits, 3-e izd., Nauka, M., 1966 | MR

[11] Boyarintsev Yu. E., Regulyarnye i singulyarnye sistemy lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, Novosibirsk, 1980 | MR | Zbl

[12] Chistyakov V. F., Algebro-differentsialnye operatory s konechnomernym yadrom, Hauka, Novosibirsk, 1996 | MR

[13] Campbell S. L., Petzold L. R., “Canonical forms and solvable singular sys of differential equations”, SIAM J. Alg. and Discrete Methods, 4:4 (1983), 517–521 | DOI | MR | Zbl

[14] Kunkel P., Mehrmann V., Differential-Algebraic Equations: Analysis and Numerical Solution, European Mathematical Society, 2006 | MR | Zbl

[15] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

[16] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Izd-vo MGU, M., 1974

[17] Polyak B. T., “Iteratsionnye metody resheniya nekorrektnykh variatsionnykh zadach”, Vychislitelnye metody i programmirovanie, Izd-vo MGU, M., 1969, 95–108

[18] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischislenii, v. II, Fizmatgiz, M., 1962

[19] Nesterov Yu. E., Vvedenie v nevypukluyu optimizatsiyu, MTsMMO, M., 2010

[20] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR | Zbl

[21] Fedorenko R. P., Vvedenie v vychislitelnuyu fiziku, 2-e izd., ispr. i dop., Izdatelskii dom “Intellekt”, Dolgoprudnyi, 2008