Geodesic
New methods for localizing discontinuities of a~noisy function
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 375-386

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

For a problem of localizing the singularities (discontinuities of the first kind) of a noisy function in $L_p$ ($1\le p\infty$), new classes of regularizing methods are constructed. These methods determine the number of discontinuities and approximate their positions. Also, upper and lower bound of the localizing singularities and the separability threshold, is obtain. It is proved that the methods are order-optimal by accuracy as well as separability on some classes of functions with discontinuities. 
@article{SJVM_2010_13_4_a1,
     author = {T. V. Antonova},
     title = {New methods for localizing discontinuities of a~noisy function},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {375--386},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a1/}
}
TY  - JOUR
AU  - T. V. Antonova
TI  - New methods for localizing discontinuities of a~noisy function
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2010
SP  - 375
EP  - 386
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a1/
LA  - ru
ID  - SJVM_2010_13_4_a1
ER  - 
%0 Journal Article
%A T. V. Antonova
%T New methods for localizing discontinuities of a~noisy function
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2010
%P 375-386
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a1/
%G ru
%F SJVM_2010_13_4_a1
T. V. Antonova. New methods for localizing discontinuities of a~noisy function. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 375-386. http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a1/