Geodesic
Regularizing algorithms for detecting discontinuities in ill-posed problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 8, pp. 1362-1370

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

The problem of detecting singularities (discontinuities of the first kind) of a noisy function in $L_2$ is considered. A wide class of regularizing algorithms that can detect discontinuities is constructed. New estimates of accuracy of determining the location of discontinuities are obtained and their optimality in terms of order with respect to the error level $\delta$ is proved for some classes of functions with isolated singularities. New upper bounds for the singularity separation threshold are obtained. 
@article{ZVMMF_2008_48_8_a2,
     author = {A. L. Ageev and T. V. Antonova},
     title = {Regularizing algorithms for detecting discontinuities in ill-posed problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1362--1370},
     publisher = {mathdoc},
     volume = {48},
     number = {8},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_8_a2/}
}
TY  - JOUR
AU  - A. L. Ageev
AU  - T. V. Antonova
TI  - Regularizing algorithms for detecting discontinuities in ill-posed problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 1362
EP  - 1370
VL  - 48
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_8_a2/
LA  - ru
ID  - ZVMMF_2008_48_8_a2
ER  - 
%0 Journal Article
%A A. L. Ageev
%A T. V. Antonova
%T Regularizing algorithms for detecting discontinuities in ill-posed problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 1362-1370
%V 48
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_8_a2/
%G ru
%F ZVMMF_2008_48_8_a2
A. L. Ageev; T. V. Antonova. Regularizing algorithms for detecting discontinuities in ill-posed problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 8, pp. 1362-1370. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_8_a2/