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.

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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/}
}
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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/