Geodesic
The exact order of information-based complexity of weakly singular integral equations with periodic analytic coefficients
Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 643-656 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The exact order of complexity of weakly singular integral equations including logarithmic singularities with periodic and analytic coefficients is found. This class of equations contains the boundary equations of exterior boundary value problems for the two-dimensional Helmholtz equation. 
@article{MZM_1997_62_5_a0,
     author = {M. Azizov},
     title = {The exact order of information-based complexity of weakly singular integral equations with periodic analytic coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--656},
     year = {1997},
     volume = {62},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a0/}
}
TY  - JOUR
AU  - M. Azizov
TI  - The exact order of information-based complexity of weakly singular integral equations with periodic analytic coefficients
JO  - Matematičeskie zametki
PY  - 1997
SP  - 643
EP  - 656
VL  - 62
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a0/
LA  - ru
ID  - MZM_1997_62_5_a0
ER  - 
%0 Journal Article
%A M. Azizov
%T The exact order of information-based complexity of weakly singular integral equations with periodic analytic coefficients
%J Matematičeskie zametki
%D 1997
%P 643-656
%V 62
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a0/
%G ru
%F MZM_1997_62_5_a0
M. Azizov. The exact order of information-based complexity of weakly singular integral equations with periodic analytic coefficients. Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 643-656. http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a0/

[1] Wozniakowski H., “Information-based complexity”, Ann. Rev. Comput. Sci., 1 (1986), 318–380 | DOI

[2] Pereverzev S. V., “O slozhnosti zadachi nakhozhdeniya reshenii uravnenii Fredgolma vtorogo roda s gladkimi yadrami, II”, Ukr. matem. zh., 41:2 (1989), 189–193 | MR

[3] Pereverzev S. V., “Giperbolicheskii krest i slozhnosti priblizhennogo resheniya integralnykh uravnenii Fredgolma vtorogo roda s differentsiruemymi yadrami”, Sib. matem. zh., 32:1 (1991), 107–115 | MR | Zbl

[4] Frank K., Heinrich S., Pereverzev S. V., Information complexity of multivariate Fredholm integral equations in Sobolev classes, Technical Report No. 263/95, Univ. Kaiserslautern, Kaiserslautern, 1995

[5] Pereverzev S. V., Sharipov C. C., “Information complexity of the equations of the second kind with compact operators in Hilbert space”, J. Complexity, 8:2 (1992), 176–202 | DOI | MR | Zbl

[6] Makhkamov K. Sh., “O slozhnosti zadachi nakhozhdeniya reshenii slabo singulyarnykh integralnykh uravnenii”, Dokl. AN Ukrainy, 1994, no. 1, 28–34 | MR | Zbl

[7] Yan Y., “A fast numerical solution for a second kind boundary integral equation with a logarithmic kernel”, SIAM J. Numer. Anal., 31:2 (1994), 477–498 | DOI | MR | Zbl

[8] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, Izd-vo MGU, M., 1976

[9] Saranen J., Vainikko G., “Trigonometric collocation methods with product integration for boundary integral equations on closed curves”, SIAM J. Numer. Anal., 32:2 (1995), 2845–2851 | MR

[10] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | Zbl