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An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems. (English) Zbl 1247.65050
The authors are concerned with the computation of a few eigenvalues and eigenvectors, near a given shift, for large sparse structured generalized eigenvalue problems of the form \(Mx = \lambda N x\), where \(M\) is a symmetric matrix and \(N\) a skew-symmetric one. Their new method improves and generalizes the SHIRA method of V. Mehrmann and D. Watkins [SIAM J. Sci. Comput. 22, No. 6, 1905–1925 (2001; Zbl 0986.65033)] to the case where the skew-symmetric matrix is singular. Applications and special properties of the new method are illustrated by benchmark problems.

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F18 Numerical solutions to inverse eigenvalue problems
65F50 Computational methods for sparse matrices
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