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 
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/
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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.

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