Interpolation by the simplest fractions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 30-37.

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

The interpolation by means of real simplest fractions is considered. There are offered a different ways of intepolating simpest fractions construction with distinct real nodes. Necessary and sufficient conditions of existence and uniqueness of interpolating simplest fractions are received. Interpolation of constants is in detail investigated; in this case the estimation of an error of interpolation on Chebyshev's system of nodes is received.
@article{ISU_2009_9_2_a5,
     author = {E. N. Kondakova},
     title = {Interpolation by the simplest fractions},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {30--37},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a5/}
}
TY  - JOUR
AU  - E. N. Kondakova
TI  - Interpolation by the simplest fractions
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2009
SP  - 30
EP  - 37
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a5/
LA  - ru
ID  - ISU_2009_9_2_a5
ER  - 
%0 Journal Article
%A E. N. Kondakova
%T Interpolation by the simplest fractions
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2009
%P 30-37
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a5/
%G ru
%F ISU_2009_9_2_a5
E. N. Kondakova. Interpolation by the simplest fractions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 2, pp. 30-37. http://geodesic.mathdoc.fr/item/ISU_2009_9_2_a5/

[1] Chui C. K., “On approximation in the Bers spaces”, Proc. Amer. Math. Soc., 40 (1973), 438–442 | DOI | MR | Zbl

[2] Chui C. K., Shen X. C., “Order of approximation by electrostatic fields due to electrons”, Constr. Approx., 1 (1985), 121–135 | DOI | MR | Zbl

[3] Danchenko V. I., Danchenko D. Ya., “O ravnomernom priblizhenii logarifmicheskimi proizvodnymi mnogochlenov”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Materialy shkoly-konf., posvyasch. 130-letiyu so dnya rozhd. D. F. Egorova, Kazan, 1999, 74–77

[4] Dolzhenko E. P., “Naiprosteishie drobi”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Materialy V Kazansk. mezhdunar. letnei shkoly-konf., Kazan, 2001, 90–94

[5] Kosukhin O. N., “Ob approksimativnykh svoistvakh naiprosteishikh drobei”, Vestnik Mosk. un-ta. Ser. 1. Matematika. Mekhanika, 2001, no. 4, 54–58 | MR

[6] Borodin P. A., “Otsenki rasstoyanii do pryamykh i luchei ot polyusov naiprosteishikh drobei, ogranichennykh po norme $L_p$ na etikh mnozhestvakh”, Mat. zametki, 82:6 (2007), 803–810 | DOI | MR | Zbl

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

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

[9] Danchenko V. I., “Ob approksimativnykh svoistvakh summ vida $\sum_k\lambda_kh(\lambda_k z)$”, Mat. zametki, 83:5 (2008), 643–649 | DOI | MR | Zbl

[10] Danchenko V. I., “Otsenki proizvodnykh naiprosteishikh drobei i drugie voprosy”, Mat. sb., 197:4 (2006), 33–52 | DOI | MR | Zbl

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

[12] Fryantsev A. V., “O polinomialnykh resheniyakh lineinykh differentsialnykh uravnenii”, UMN, 63:3(381) (2008), 149–150 | DOI | MR | Zbl

[13] Demidovich B. P., Maron I. A., Osnovy vychislitelnoi matematiki, Fizmatgiz, M., 1963, 660 pp. | MR

[14] Fikhtengolts G. M., Osnovy matematicheskogo analiza, Lan, SPb., M., Krasnodar, 2005, 512 pp.

[15] Prasolov V. V., Mnogochleny, Fizmatlit, M., 2002, 453 pp.

[16] Kurosh A. G., Kurs vysshei algebry, v. Lan, SPb., 2004, 432 pp.