Geodesic
On orthorecursive expansions with errors in the calculation of coefficients
Izvestiya. Mathematics , Tome 69 (2005) no. 1, pp. 1-14.

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

We study orthorecursive expansions with errors in the calculation of coefficients. We prove that if a system of elements in a space with scalar product satisfies certain requirements, then the orthorecursive expansion with respect to this system is absolutely stable under a large class of relative and absolute numerical errors. It is also stable under small perturbations of the system. 
@article{IM2_2005_69_1_a0,
     author = {V. V. Galatenko},
     title = {On orthorecursive expansions with errors in the calculation of coefficients},
     journal = {Izvestiya. Mathematics },
     pages = {1--14},
     publisher = {mathdoc},
     volume = {69},
     number = {1},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_1_a0/}
}
TY  - JOUR
AU  - V. V. Galatenko
TI  - On orthorecursive expansions with errors in the calculation of coefficients
JO  - Izvestiya. Mathematics 
PY  - 2005
SP  - 1
EP  - 14
VL  - 69
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2005_69_1_a0/
LA  - en
ID  - IM2_2005_69_1_a0
ER  - 
%0 Journal Article
%A V. V. Galatenko
%T On orthorecursive expansions with errors in the calculation of coefficients
%J Izvestiya. Mathematics 
%D 2005
%P 1-14
%V 69
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2005_69_1_a0/
%G en
%F IM2_2005_69_1_a0
V. V. Galatenko. On orthorecursive expansions with errors in the calculation of coefficients. Izvestiya. Mathematics , Tome 69 (2005) no. 1, pp. 1-14. http://geodesic.mathdoc.fr/item/IM2_2005_69_1_a0/

[1] Lukashenko T. P., “Ob ortorekursivnykh razlozheniyakh po sisteme Fabera–Shaudera”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tezisy dokladov 10-i Saratovskoi zimnei shkoly, Izd-vo Saratovskogo un-ta, Saratov, 2000, 83

[2] Lukashenko T. P., “O svoistvakh ortorekursivnykh razlozhenii po neortogonalnym sistemam”, Vestn. Mosk. un-ta. Ser. 1. Matematika. Mekhanika, 2001, no. 1, 6–10 | MR | Zbl

[3] Gribonval R., Nielsen M., “Approximate Weak Greedy Algorithms”, Adv. Comput. Math., 14:4 (2001), 361–378 | DOI | MR | Zbl

[4] Temlyakov V. N., “Weak greedy algorithms”, Adv. Comput. Math., 12:2, 3 (2000), 213–227 | DOI | MR | Zbl

[5] Kudryavtsev A. Yu., “Ortorekursivnye razlozheniyakh po sistemam szhatii i sdvigov”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tezisy dokladov 11-i Saratovskoi zimnei shkoly, Izd-vo GosUNTs “Kolledzh”, Saratov, 2002, 106–108

[6] Kudryavtsev A. Yu., “Ortorekursivnye razlozheniyakh po sistemam neortogonalnykh vspleskov”, Sovremennye metody teorii funktsii i smezhnye problemy, Materialy konferentsii, Voronezh. gos. un-t, Voronezh, 2003, 137–138

[7] Bari N. K., “Ob ustoichivosti svoistva polnoty sistemy funktsii”, Dokl. AN SSSR, 37 (1942), 99–103

[8] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, t. 1, izd. 7-e, Nauka, M., 1969