Geodesic
Methods of identifying a parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 107-120 
T. V. Antonova. Methods of identifying a parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 107-120. http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a0/
@article{SJVM_2015_18_2_a0,
     author = {T. V. Antonova},
     title = {Methods of identifying a~parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {107--120},
     year = {2015},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a0/}
}
TY  - JOUR
AU  - T. V. Antonova
TI  - Methods of identifying a parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2015
SP  - 107
EP  - 120
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a0/
LA  - ru
ID  - SJVM_2015_18_2_a0
ER  - 
%0 Journal Article
%A T. V. Antonova
%T Methods of identifying a parameter in the kernel of the first kind equation of the convolution type on the class of functions with discontinuities
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2015
%P 107-120
%V 18
%N 2
%U http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a0/
%G ru
%F SJVM_2015_18_2_a0

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

In this paper, we propose a regular iterative method of identifying a numerical parameter in the kernel of the integral equation of the first kind of the convolution type. It is shown that an unambiguous identification of the parameter is possible when an exact solution has discontinuities of the first kind. The convergence theorem is proved, and an example of the equation with a parameter, for which the method constructed is applicable, is given.

[1] Bejts R., Mak-Donnel M., Vosstanovlenie i rekonstruktsiya izobrazhenij, Mir, M., 1989

[2] Vasilenko G. I., Taratorin A. M., Vosstanovlenie izobrazhenij, Radio i svyaz', M., 1986

[3] Protasov K. T., Belov V. V., Molchunov N. V., “Vosstanovlenie izobrazhenij s predvaritel'nym otsenivaniem funktsii rasseyaniya tochki”, Optika atmosfery i okeana, 13:2 (2000), 139–145

[4] Ageev A. L., Antonova T. V., “On solution of nonlinear with respect to parameter equation of the first kind on the class of discontinuous functions”, J. Inverse and Ill-Posed Problems, 7:1 (1999), 1–16 | MR | Zbl

[5] Antonova T. V., “O reshenii nelinejnykh po parametru uravnenij 1 roda na klassakh obobshchennykh funktsii”, Zhurn. vychisl. matematiki i mat. fiziki, 40:6 (2000), 819–831 | MR | Zbl

[6] Antonova T. V., “Reshenie uravnenij pervogo roda na klassakh funktsij s osobennostyami”, Tr. in-ta matematiki i mekhaniki UrO RAN, 8, no. 1, 2002, 147–188 | MR | Zbl

[7] Antonova T. V., Dep. v VINITI 17.10.00, No 2639-V00, IMM UrO RAN, Ekaterinburg, 2000

[8] Hall P., Qui P., “Blind deconvolution and deblurring in image analysis”, Statistica Sinica, 17 (2007), 1483–1509 | MR | Zbl

[9] Ageev A. L., Antonova T. V., “O nekorrektno postavlennykh zadachakh lokalizatsii osobennostej”, Tr. in-ta matematiki i mekhaniki UrO RAN, 17, no. 3, 2011, 30–45