Geodesic
The incomplete block decomposition based on Pade approximants
Matematičeskoe modelirovanie, Tome 18 (2006) no. 4, pp. 89-99.

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

In this paper, we present a preconditioner for large systems of linear equations based on the incomplete block decomposition for block tridiagonal matrices. This method generalizes methods developed previously. Practical realization of this method for the model problem is similar to the realization of the method of complete matrix factorization. For more general matrices it is similar to the realization of the method constructed by one of the authors. However, in both cases the regarded method is more effective then the last ones. 
@article{MM_2006_18_4_a6,
     author = {A. A. Buzdin and E. A. Vasilieva},
     title = {The incomplete block decomposition  based on {Pade} approximants},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {89--99},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_4_a6/}
}
TY  - JOUR
AU  - A. A. Buzdin
AU  - E. A. Vasilieva
TI  - The incomplete block decomposition  based on Pade approximants
JO  - Matematičeskoe modelirovanie
PY  - 2006
SP  - 89
EP  - 99
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2006_18_4_a6/
LA  - ru
ID  - MM_2006_18_4_a6
ER  - 
%0 Journal Article
%A A. A. Buzdin
%A E. A. Vasilieva
%T The incomplete block decomposition  based on Pade approximants
%J Matematičeskoe modelirovanie
%D 2006
%P 89-99
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2006_18_4_a6/
%G ru
%F MM_2006_18_4_a6
A. A. Buzdin; E. A. Vasilieva. The incomplete block decomposition  based on Pade approximants. Matematičeskoe modelirovanie, Tome 18 (2006) no. 4, pp. 89-99. http://geodesic.mathdoc.fr/item/MM_2006_18_4_a6/

[1] Buzdin A., “Tangential decomposition”, Computing, 61 (1998), 257–276 | DOI | MR | Zbl

[2] Buzdin A., Wittum G., “Two-Frequency Decomposition”, Numer. Math., 97 (2004), 269–295 | DOI | MR | Zbl

[3] Buzdin A. A., Vasileva E. A., “Ob odnom variante metoda nepolnogo blochnogo razlozheniya”, Vestnik Kaliningradskogo Gosudarstvennogo Universiteta, 2005, no. 1–2. Ser. Informatika i telekommunikatsii, 70–76

[4] Buzdin A., Logashenko D., “Incomplete Block Triangular Decompositions of Order I”, Computing, 64 (2000), 69–95 | DOI | MR | Zbl

[5] Samarskii A. A, Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[6] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1977 | MR | Zbl

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

[8] Axelson O., Polman B., “A robust preconditioner based on algebraic substructuring and two-level grids”, Robust multigrid methods, NNFM Bd.23, ed. W. Hackbusch, Vieweg-Verlag, Braunschweig, 1989 | MR

[9] Wittum G., “Filternde Zerlegungen – Schnelle Löser für grosse Gleichungssysteme”, Teubner Skripten zur Numerik, Band 1, Teubner-Verlag, Stuttgart, 1992 | MR | Zbl

[10] Wagner C., “Tangential frequency filtering decompositions for symmetric matrices”, Numer. Math., 78 (1997), 143–163 | DOI | MR | Zbl

[11] Kettler R., “Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods”, Multigrid methods, Proceedings, eds. W. Hackbusch, U. Trottenberg, Köln-Porz, 1981 ; Springer-Verlag, Berlin, 1982 | MR

[12] Stoer J., Bulirsch R., Introduction to numerical analysis, Springer-Verlag, New York, 1992

[13] Baker G. A. Jr., Essentials of Padé Approximants, Academic Press, New York, 1975 | MR

[14] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973 | MR

[15] Akhiezer N. I., Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, Fizmatgiz, M., 1961 | MR