Geodesic
An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix
Numerical methods and programming, Tome 17 (2016) no. 1, pp. 44-54

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

An efficient version of the conjugate direction method to find a nontrivial solution of a homogeneous system of linear algebraic equations with a singular symmetric nonnegative definite square matrix is proposed and substantiated. A one-parameter family of one-step nonlinear iterative processes to determine the eigenvector corresponding to the largest eigenvalue of a symmetric nonnegative definite square matrix is also proposed. This family includes the power method as a special case. The convergence of corresponding vector sequences to the eigenvector associated with the largest eigenvalue of the matrix is proved. A two-step procedure is formulated to accelerate the convergence of iterations for these processes. This procedure is based on the orthogonalization in Krylov subspaces. A number of numerial results are discussed.
Keywords: eigenvector, eigenvalue, conjugate direction method, Krylov subspaces. 
@article{VMP_2016_17_1_a4,
     author = {I. V. Kireev},
     title = {An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix},
     journal = {Numerical methods and programming},
     pages = {44--54},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a4/}
}
TY  - JOUR
AU  - I. V. Kireev
TI  - An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix
JO  - Numerical methods and programming
PY  - 2016
SP  - 44
EP  - 54
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a4/
LA  - ru
ID  - VMP_2016_17_1_a4
ER  - 
%0 Journal Article
%A I. V. Kireev
%T An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix
%J Numerical methods and programming
%D 2016
%P 44-54
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a4/
%G ru
%F VMP_2016_17_1_a4
I. V. Kireev. An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix. Numerical methods and programming, Tome 17 (2016) no. 1, pp. 44-54. http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a4/