Abstract
Matrix eigenvalue problems are frequently encountered in engineering and science. In this paper, we propose an extended shift-invert residual Arnoldi method for solving some smaller eigenvalues and the corresponding eigenvectors of a large and symmetric matrix, based on the idea of perfect Krylov subspace method proposed by Bai and Miao. We prove that the projected subspace of the proposed method is the same as the perfect Krylov subspace in exact computation. Based on this result, we also prove the convergence of the proposed method. Numerical experiments show that this method is superior to the perfect Krylov subspace method and the shift-invert residual Arnoldi method.
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Communicated by Jinyun Yuan.
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Yue, SF., Zhang, JJ. An extended shift-invert residual Arnoldi method. Comp. Appl. Math. 40, 63 (2021). https://doi.org/10.1007/s40314-021-01444-3
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DOI: https://doi.org/10.1007/s40314-021-01444-3