Geodesic
On incomplete factorization for the fast Fourier transform for the discrete Poisson equation in a~curvilinear boundary domain
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 3, pp. 197-216.

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

For the discrete Laplasian on the rectangular grid the spectral equivalent preconditioner of the type of the incomplete block-factorization is constructed. The inversion of this preconditioner with accuracy $\varepsilon=O(N^{-1})$ is realized with the help of the fast Fourier transform with $O(N\ln N\ln(1/\varepsilon))$ arithmetical operations. 
@article{SJVM_1998_1_3_a0,
     author = {I. A. Blatov},
     title = {On incomplete factorization for the fast {Fourier} transform for the discrete {Poisson} equation in a~curvilinear boundary domain},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {197--216},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_3_a0/}
}
TY  - JOUR
AU  - I. A. Blatov
TI  - On incomplete factorization for the fast Fourier transform for the discrete Poisson equation in a~curvilinear boundary domain
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1998
SP  - 197
EP  - 216
VL  - 1
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_1998_1_3_a0/
LA  - ru
ID  - SJVM_1998_1_3_a0
ER  - 
%0 Journal Article
%A I. A. Blatov
%T On incomplete factorization for the fast Fourier transform for the discrete Poisson equation in a~curvilinear boundary domain
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1998
%P 197-216
%V 1
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_1998_1_3_a0/
%G ru
%F SJVM_1998_1_3_a0
I. A. Blatov. On incomplete factorization for the fast Fourier transform for the discrete Poisson equation in a~curvilinear boundary domain. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 3, pp. 197-216. http://geodesic.mathdoc.fr/item/SJVM_1998_1_3_a0/

[1] Samarskii A. A., Nikolaev E. N., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[2] Ilin V. P., Metody nepolnoi faktorizatsii dlya resheniya algebraicheskikh sistem, Nauka, M., 1995 | MR

[3] Notay Y., Ould Omar Z., “Incomplete factorization preconditioning may lead to multigrid like speed of convergence”, Proc. of the Intern. Conf. AMCA-95 (Novosibirsk, 1995), 435–446 | MR

[4] Notay Y., “A multilevel method that does not require the hierarchical basis”, Mezhdunarodnaya algebraicheskaya konferentsiya pamyati D. K. Faddeeva (Sankt-Peterburg, 1997), 92 | Zbl

[5] Larin M. R., Algebraic multilevel incomplete factorization methoods for five point matrices, Report No 636, University of Nijmegen, Departament of Mathematics, 1996

[6] Blatov I. A., “Ob algebrakh operatorov s psevdorazrezhennymi matritsami i ikh prilozheniyakh”, Sib. mat. zhurn., 37:1 (1996), 36–59 | MR | Zbl

[7] Blatov I. A., “Ob otsenkakh elementov $LU$-razlozhenii razrezhennykh matrits i ikh prilozheniyakh k metodam nepolnoi faktorizatsii”, Zhurn. vychisl. matem. i mat. fiz., 37:3 (1997), 259–276 | MR | Zbl

[8] Voevodin V. V., Kuznetsov Yu. A., Matritsy i vychisleniya, Nauka, M., 1984 | MR | Zbl

[9] Berg I., Lefstrem I., Interpolyatsionnye prostranstva, Mir, M., 1980 | MR