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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.

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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