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Your search keyword '"Zhou, Yunkai"' showing total 2 results
Start Over Author "Zhou, Yunkai" Topic eigenvalue Topic eigenvalues
2 results on '"Zhou, Yunkai"'

1. On the eigenvalues of specially low-rank perturbed matrices

Author

Zhou, Yunkai

Subjects
*EIGENVALUES, *PERTURBATION theory, *MATRICES (Mathematics), *INVARIANT subspaces, *EIGENVECTORS, *GENERALIZATION, *MATHEMATICAL analysis, *NUMERICAL analysis
Abstract

Abstract: We study the eigenvalues of a matrix A perturbed by a few special low-rank matrices. The perturbation is constructed from certain basis vectors of an invariant subspace of A, such as eigenvectors, Jordan vectors, or Schur vectors. We show that most of the eigenvalues of the low-rank perturbed matrix stayed unchanged from the eigenvalues of A; the perturbation can only change the eigenvalues of A that are related to the invariant subspace. Existing results mostly studied using eigenvectors with full column rank for perturbations, we generalize the results to more general settings. Applications of our results to a few interesting problems including the Google’s second eigenvalue problem are presented. [Copyright &y& Elsevier]

Published
2011
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2. Computing eigenvalue bounds for iterative subspace matrix methods

Author

Zhou, Yunkai, Shepard, Ron, and Minkoff, Michael

Subjects
*MATRICES (Mathematics), *EIGENVALUES, *HILL determinant, *HOUGH functions
Abstract

Abstract: A procedure is presented for the computation of bounds to eigenvalues of the generalized hermitian eigenvalue problem and to the standard hermitian eigenvalue problem. This procedure is applicable to iterative subspace eigenvalue methods and to both outer and inner eigenvalues. The Ritz values and their corresponding residual norms, all of which are computable quantities, are needed by the procedure. Knowledge of the exact eigenvalues is not needed by the procedure, but it must be known that the computed Ritz values are isolated from exact eigenvalues outside of the Ritz spectrum and that there are no skipped eigenvalues within the Ritz spectrum range. A multipass refinement procedure is described to compute the bounds for each Ritz value. This procedure requires effort where m is the subspace dimension for each pass. [Copyright &y& Elsevier]

Published
2005
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