Geodesic
Convergence analysis of an optimization algorithm for computing
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 5-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A new optimization algorithm for computing the largest eigenvalue of a real symmetric matrix is considered. The algorithm is based on a sequence of plane rotations increasing the sum of the matrix entries. It is proved that the algorithm converges linearly and it is shown that it can be regarded as a relaxation method for the Rayleigh quotient. 
@article{ZNSL_2007_346_a0,
     author = {A. N. Borzykh},
     title = {Convergence analysis of an optimization algorithm for computing},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--20},
     year = {2007},
     volume = {346},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a0/}
}
TY  - JOUR
AU  - A. N. Borzykh
TI  - Convergence analysis of an optimization algorithm for computing
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 5
EP  - 20
VL  - 346
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a0/
LA  - ru
ID  - ZNSL_2007_346_a0
ER  - 
%0 Journal Article
%A A. N. Borzykh
%T Convergence analysis of an optimization algorithm for computing
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 5-20
%V 346
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a0/
%G ru
%F ZNSL_2007_346_a0
A. N. Borzykh. Convergence analysis of an optimization algorithm for computing. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 5-20. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a0/

[1] Dzh. Kh. Uilkinson, Algebraicheskaya problema sobstvennykh znachenii, Nauka, M., 1970

[2] D. K. Faddeev, V. N. Faddeeva, Vychislitelnye metody lineinoi algebry, Lan, SPb., 2002

[3] B. Parlett, Simmetrichnaya problema sobstvennykh znachenii, Mir, M., 1983 | MR | Zbl

[4] Kh. D. Ikramov, Nesimmetrichnaya problema sobstvennykh znachenii, Nauka, M., 1991 | MR

[5] Dzh. Demmel, Vychislitelnaya lineinaya algebra, Mir, M., 2001

[6] A. N. Borzykh, “Effektivnaya lokalizatsiya sobstvennykh znachenii simmetrichnykh matrits vysokogo poryadka”, Nauchnaya sessiya MIFI-2006, Sbornik nauchnykh trudov. Tom 7, Izd. MIFI, M., 2006, 159–160