Geodesic
Approximation of finite-section equations by piecewise constant functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 731-745 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem is studied of reducing the amount of discrete information required for achieving a prescribed accuracy of solving Fredholm integral equations of the first kind on a half-line. The equations are solved by the finite-section method combined with piecewise constant interpolation of the kernel and the right-hand side at uniform grid points. The approximating properties of the discretization schemes are examined, and the corresponding computational costs are analyzed. 
@article{ZVMMF_2008_48_5_a0,
     author = {E. V. Lebedeva and S. G. Solodkii},
     title = {Approximation of finite-section equations by piecewise constant functions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {731--745},
     year = {2008},
     volume = {48},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a0/}
}
TY  - JOUR
AU  - E. V. Lebedeva
AU  - S. G. Solodkii
TI  - Approximation of finite-section equations by piecewise constant functions
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 731
EP  - 745
VL  - 48
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a0/
LA  - ru
ID  - ZVMMF_2008_48_5_a0
ER  - 
%0 Journal Article
%A E. V. Lebedeva
%A S. G. Solodkii
%T Approximation of finite-section equations by piecewise constant functions
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 731-745
%V 48
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a0/
%G ru
%F ZVMMF_2008_48_5_a0
E. V. Lebedeva; S. G. Solodkii. Approximation of finite-section equations by piecewise constant functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 731-745. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a0/

[1] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya nekorrektno postavlennykh zadach i prilozheniya, Nauka, M., 1978

[2] Tikhonov A. N., Goncharskii A. B., Stepanov V. V., Yagola A. G., Regulyarizuyuschie algoritmy i apriornaya informatsiya, Nauka, M., 1983 | MR

[3] Morozov V. A., Regulyarnye metody resheniya nekorrektno postavlennykh zadach, Nauka, M., 1987 | MR

[4] Bakushinskii A. B., Goncharskii A. B., Iterativnye metody resheniya nekorrektnykh zadach, Izd-vo MGU, M., 1989 | MR

[5] Vasin V. V., Ageev A. A., Nekorrektnye zadachi s apriornoi informatsiei, Uralskoe izd-vo Nauka, Ekaterinburg, 1993 | MR

[6] Engl H. W., Hanke M., Neubauer A., Regularization of inverse problems, Kluwer Acad. Publ., Dordrecht, Boston, London, 1996 | MR | Zbl

[7] Solodkii S. G., “Optimizatsiya proektsionnykh metodov resheniya lineinykh nekorrektnykh zadach”, Zh. vych. chisl. matem. i matem. fiz., 39:2 (1999), 195–203 | MR

[8] Vilenkin N. Ya., Gorin E. A. i dr., Funktsionalnyi analiz, ed. S. G. Krein, Nauka, M., 1964 | Zbl

[9] Bertero M., Pike E., “Exponential-sampling method for Laplace and other dilationally invariant transforms. II. Examples in photon correlation spectroscopy and Fraunhofer diffraction”, Inverse Problems, 7 (1991), 21–41 | DOI | MR | Zbl

[10] Pereverzev S., Schock E., “The finite-section approximation for ill-posed integral equations on the half-line”, J. Integral Equations Appl., 11 (2001), 501–513 | DOI | MR

[11] Bidinger G., Schock E., “Integral equations of the first kind on the half-line”, Numer. Methods and Optimizat. Tallinn, 3 (1992), 4–11 | MR

[12] Plato R., Vainikko G., “On the regularization of projection methods for solving ill-posed problems”, Numer. Math., 57 (1990), 63–79 | DOI | MR | Zbl

[13] Bakushinskii A. B., “Odin obschii priem postroeniya regulyarizuyuschikh algoritmov dlya lineinogo nekorrektnogo uravneniya v gilbertovom prostranstve”, Zh. vychisl. matem. i matem. fiz., 7:3 (1967), 672–677

[14] Vainikko G. M., Veretennikov A. Yu., Iteratsionnye protsedury v nekorrektnykh zadachakh, Nauka, M., 1986 | MR