Parallel decomposition version in the AISM preconditioner
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 120-126.

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

We propose a variant of the parallel decomposition in the formation of preconditioner based on the approximate inversion of the Sherman-Morrison. We conduct numerical experiments for solving test systems of equations using GPUs.
Keywords: solving systems of linear algebraic equations, preconditioners, parallel algorithms, graphics processing.
@article{IIMI_2015_46_2_a15,
     author = {N. S. Nedozhogin and S. P. Kopysov and A. K. Novikov},
     title = {Parallel decomposition version in the {AISM} preconditioner},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {120--126},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a15/}
}
TY  - JOUR
AU  - N. S. Nedozhogin
AU  - S. P. Kopysov
AU  - A. K. Novikov
TI  - Parallel decomposition version in the AISM preconditioner
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2015
SP  - 120
EP  - 126
VL  - 46
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a15/
LA  - ru
ID  - IIMI_2015_46_2_a15
ER  - 
%0 Journal Article
%A N. S. Nedozhogin
%A S. P. Kopysov
%A A. K. Novikov
%T Parallel decomposition version in the AISM preconditioner
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2015
%P 120-126
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a15/
%G ru
%F IIMI_2015_46_2_a15
N. S. Nedozhogin; S. P. Kopysov; A. K. Novikov. Parallel decomposition version in the AISM preconditioner. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 46 (2015) no. 2, pp. 120-126. http://geodesic.mathdoc.fr/item/IIMI_2015_46_2_a15/

[1] Saad Y., Iterative methods for sparse linear systems, SIAM, 2003, xviii+528 pp. | MR | Zbl

[2] Benzi M., “Preconditioning techniques for large linear systems: a survey”, Journal of Computational Physics, 182:2 (2002), 418–477 | DOI | MR | Zbl

[3] Kolotilina L. Yu., Yeremin A. Yu., “Factorized sparse approximate inverse preconditionings. I: Theory”, SIAM Journal on Matrix Analysis and Applications, 14:1 (1993), 45–58 | DOI | MR | Zbl

[4] Grote M., Huckle T., “Parallel preconditioning with sparse approximate inverses”, SIAM Journal on Scientific Computing, 18:3 (1997), 838–853 | DOI | MR | Zbl

[5] Sherman J., Morrison W. J., “Adjustment of an inverse matrix corresponding to a change in one element of a given matrix”, The Annals of Mathematical Statistics, 21:1 (1950), 124–127 | DOI | MR | Zbl

[6] Nedozhogin N. S., Kopysov S. P., Novikov A. K., “Parallel forming preconditioner based on the approximate Sherman–Morrison inversion”, Vychislitel'nye metody i programmirovanie, 16 (2015), 86–93 (in Russian)

[7] Bru M., Cerdán J., Marín J., Mas J., “Preconditioning sparse nonsymmetric linear systems with Sherman–Morrison formula”, SIAM Journal on Scientific Computing, 25:2 (2003), 701–715 | DOI | MR | Zbl