Geodesic
An incomplete factorization method with the fast Fourier transform for discrete Poisson equations with different boundary conditions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 3, pp. 229-242.

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For the discrete Laplacian on a rectangular grid with Dirichlet and Dirichlet-Neumann boundary conditions, a spectral equivalent preconditioner of incomplete block-factorization type is constructed. The inversion of this preconditioner is realized with the help of the fast Fourier transform with $O(N\ln N)$ arithmetical operations. 
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I. A. Blatov; E. V. Kitaeva. An incomplete factorization method with the fast Fourier transform for discrete Poisson equations with different boundary conditions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 3, pp. 229-242. http://geodesic.mathdoc.fr/item/SJVM_2001_4_3_a1/

[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”, Proceeding of the International Conference AMGA-95 (June 20–24, 1995), NCC Publisher, Novosibirsk, 1995, 435–446 | MR

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

[5] Larin M. R., Algebraic multilevel incomplete factorization methods for five point matrices, Report / Departament of Mathematics University of Nijmegen; 9636, December, Nijmegen, 1996

[6] Blatov I. A., “O metode nepolnoi blochnoi faktorizatsii v sochetanii s bystrym preobrazovaniem Fure resheniya diskretnogo uravneniya Puassona v oblasti s krivolineinoi granitsei”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie. — Novosibirsk, 1:3 (1998), 197–216 | MR | Zbl

[7] Blatov I. A., “Ob asimptoticheski tochnykh otsenkakh predobuslavlivatelei tipa nepolnoi blochnoi faktorizatsii”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie, 3:1 (2000), 11–42 | MR | Zbl

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

[9] Andreev V. B., “Ustoichivost raznostnykh skhem dlya ellipticheskikh uravnenii po granichnym usloviyam Dirikhle”, Zhurn. vychisl. matem. i mat. fiziki, 12:3 (1971), 598–611

[10] Matsokin A. M., Nepomnyaschikh S. V., “Primenenie okaimleniya pri reshenii sistem setochnykh uravnenii”, Vychisl. algoritmy v zadachakh matem. fiziki, AN SSSR. Sib. otd-nie, Novosibirsk, 1983, 99–109