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Num. Meth. Prog., 2016, Volume 17, Issue 1, Pages 44–54 (Mi vmp814)  

This article is cited in 1 scientific paper (total in 1 paper)

An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix

I. V. Kireev

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk

Abstract: 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.

Full text: PDF file (801 kB)
UDC: 519.614
Received: 12.01.2016

Citation: I. V. Kireev, “An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix”, Num. Meth. Prog., 17:1 (2016), 44–54

Citation in format AMSBIB
\Bibitem{Kir16}
\by I.~V.~Kireev
\paper An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix
\jour Num. Meth. Prog.
\yr 2016
\vol 17
\issue 1
\pages 44--54
\mathnet{http://mi.mathnet.ru/vmp814}


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    This publication is cited in the following articles:
    1. I. V. Kireev, “Ortogonalnye proektory i sistemy lineinykh algebraicheskikh uravnenii”, Sib. zhurn. vychisl. matem., 23:3 (2020), 315–324  mathnet  crossref
  • Numerical methods and programming
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