Geodesic
On a nontraditional method of approximation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 281-287 
P. V. Chunaev. On a nontraditional method of approximation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 281-287. http://geodesic.mathdoc.fr/item/TM_2010_270_a21/
@article{TM_2010_270_a21,
     author = {P. V. Chunaev},
     title = {On a~nontraditional method of approximation},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {281--287},
     year = {2010},
     volume = {270},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a21/}
}
TY  - JOUR
AU  - P. V. Chunaev
TI  - On a nontraditional method of approximation
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2010
SP  - 281
EP  - 287
VL  - 270
UR  - http://geodesic.mathdoc.fr/item/TM_2010_270_a21/
LA  - ru
ID  - TM_2010_270_a21
ER  - 
%0 Journal Article
%A P. V. Chunaev
%T On a nontraditional method of approximation
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2010
%P 281-287
%V 270
%U http://geodesic.mathdoc.fr/item/TM_2010_270_a21/
%G ru
%F TM_2010_270_a21

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We study the approximation of functions $f(z)$ that are analytic in a neighborhood of zero by finite sums of the form $H_n(z)=H_n(h,f,\{\lambda_k\};z)=\sum_{k=1}^n\lambda_kh(\lambda_kz)$, where $h$ is a fixed function that is analytic in the unit disk $|z|1$ and the numbers $\lambda_k$ (which depend on $h,f$, and $n$) are calculated by a certain algorithm. An exact value of the radius of the convergence $H_n(z)\to f(z)$, $n\to\infty$, and an order-sharp estimate for the rate of this convergence are obtained; an application to numerical analysis is given.

[1] Danchenko V.I., “Ob approksimativnykh svoistvakh summ vida $\sum _k\lambda _kh(\lambda _kz)$”, Mat. zametki, 83:5 (2008), 643–649 | DOI | MR | Zbl

[2] Danchenko V.I., Danchenko D.Ya., “O ravnomernom priblizhenii logarifmicheskimi proizvodnymi mnogochlenov”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Mater. shk.-konf., posv. 130-letiyu so dnya rozhdeniya D.F. Egorova (Kazan, 1999 g.), Izd-vo Kazan. un-ta, Kazan, 1999, 74–77

[3] Danchenko V.I., Danchenko D.Ya., “O priblizhenii naiprosteishimi drobyami”, Mat. zametki, 70:4 (2001), 553–559 | DOI | MR | Zbl

[4] Kosukhin O.N., “Ob approksimativnykh svoistvakh naiprosteishikh drobei”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 2001, no. 4, 54–59 | MR | Zbl

[5] Borodin P.A., Kosukhin O.N., “O priblizhenii naiprosteishimi drobyami na deistvitelnoi osi”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 2005, no. 1, 3–8 | MR | Zbl

[6] Borodin P.A., “Priblizhenie naiprosteishimi drobyami na poluosi”, Mat. sb., 200:8 (2009), 25–44 | DOI | MR | Zbl

[7] Protasov V.Yu., “Priblizheniya naiprosteishimi drobyami i preobrazovanie Gilberta”, Izv. RAN. Ser. mat., 73:2 (2009), 123–140 | DOI | MR | Zbl

[8] Fryantsev A.V., “O chislennoi approksimatsii differentsialnykh polinomov”, Izv. Sarat. un-ta. Matematika. Mekhanika. Informatika, 7:2 (2007), 39–43

[9] Chunaev P.V., “Ob approksimatsii $\lambda $-summami”, Mezhdunar. konf. po matematicheskoi teorii upravleniya i mekhanike (Suzdal, 2009), Tez. dokl., MIRAN, M., 2009, 147–148

[10] Kurosh A.G., Kurs vysshei algebry, 7-e izd., Fizmatgiz, M., 1962 | MR