Composite orthogonal projection methods for large matrix eigenproblems |
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Authors: | Jia Zhongxiao |
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Institution: | (1) Department of Applied Mathematics, Dalian University of Technology, 116024 Dalian, China |
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Abstract: | For classical orthogonal projection methods for large matrix eigenproblems, it may be much more difficult for a Ritz vector
to converge than for its corresponding Ritz value when the matrix in question is non-Hermitian. To this end, a class of new
refined orthogonal projection methods has been proposed. It is proved that in some sense each refined method is a composite
of two classical orthogonal projections, in which each refined approximate eigenvector is obtained by realizing a new one
of some Hermitian semipositive definite matrix onto the same subspace. Apriori error bounds on the refined approximate eigenvector are established in terms of the sine of acute angle of the normalized
eigenvector and the subspace involved. It is shown that the sufficient conditions for convergence of the refined vector and
that of the Ritz value are the same, so that the refined methods may be much more efficient than the classical ones.
Project supported by the China State Major Key Projects for Basic Researches, the National Natural Science Foundation of China
(Grant No. 19571014), the Doctoral Program (97014113), the Foundation of Excellent Young Scholors of Ministry of Education,
the Foundation of Returned Scholars of China and the Liaoning Province Natural Science Foundation. |
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Keywords: | classical orthogonal projection refined orthogonal projection Ritz values Ritz vectors refined approximate eigenvectors convergence |
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