Geodesic
Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 983-995 
Yu. V. Bychenkov. Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 983-995. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a2/
@article{ZVMMF_2006_46_6_a2,
     author = {Yu. V. Bychenkov},
     title = {Optimization of the generalized method of {Hermitian} and {skew-Hermitian} splitting iterations for solving symmetric saddle-point problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {983--995},
     year = {2006},
     volume = {46},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a2/}
}
TY  - JOUR
AU  - Yu. V. Bychenkov
TI  - Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 983
EP  - 995
VL  - 46
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a2/
LA  - ru
ID  - ZVMMF_2006_46_6_a2
ER  - 
%0 Journal Article
%A Yu. V. Bychenkov
%T Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 983-995
%V 46
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a2/
%G ru
%F ZVMMF_2006_46_6_a2

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

An algorithm for solving a nonsingular symmetric system of linear equations with a saddle point is examined. This algorithm has two constant iteration parameters and is an extension of the algorithm of Hermitian and skew-Hermitian splitting iterations (the HSS algorithm). Analytical formulas are derived for the optimal values of the iteration parameters. The formulation of the optimization problem is a classical one for the saddle-point problems. The results obtained are sharp.

[1] Benzi M., Golub G. H., Liesen J., “Numerical solution of saddle point problems”, Acta Numerica, 14 (2005), 1–137 | DOI | MR | Zbl

[2] Benzi M., Simoncini V., On the Eigenvalues of a class of saddle point matrices, Techn. Rept. TR-2005-007-A, Dep. Math. and Comput. Sci. Emory Univ., Atlanta, GA, May 2005, 1–21 pp. | MR

[3] Benzi M., Golub G. H., “A preconditioner for generalized saddle point problems”, SIAM J. Matrix Analys. and Applic., 26:1 (2004), 20–41 | DOI | MR | Zbl

[4] Benzi M., Gander M. J., Golub G. H., “Optimization of the Hermitian and skew-hermitian splitting iteration for saddle-point problems”, BIT, 43 (2003), 881–900 | DOI | MR | Zbl

[5] Benzi M., Simoncini V., “Spectral properties of the Hermitian and skew-hermitian splitting preconditioner for saddle point problems”, SIAM J. Matrix Analys. and Applic., 26:2 (2004), 377–389 | DOI | MR | Zbl

[6] Bai Zhong-Zhi, Golub G. H., Generalized preconditioned Hermitian and skew-hermitian splitting iteration methods for saddle-point problems, SCCM Repts No 7, 2004

[7] Demyanov V. F., Malozemov B. H., Vvedenie v minimaks, Nauka, M., 1972 | MR

[8] Bychenkov Yu. V., “Optimization of one class of nonsymmetrizable algorithms for saddle point problems”, Rus. J. Numer. Analys. and Math. Modeling, 17:6 (2002), 521–546 | MR | Zbl

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

[10] Chizhonkov E. V., Relaksatsionnye metody resheniya sedlovykh zadach, IVM RAN, M., 2002