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
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.
eigenvector, eigenvalue, conjugate direction method, Krylov subspaces.
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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
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\paper An orthogonal power method of solving the partial eigenproblem for a symmetric nonnegative definite matrix
\jour Num. Meth. Prog.
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This publication is cited in the following articles:
I. V. Kireev, “Ortogonalnye proektory
i sistemy lineinykh algebraicheskikh uravnenii”, Sib. zhurn. vychisl. matem., 23:3 (2020), 315–324
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