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Computational error bounds for multiple or nearly multiple eigenvalues. (English) Zbl 0986.65031

The bounds for clusters of eigenvalues of nonselfadjoint matrices are investigated. A method for the computation of rigorous error bounds for multiple or nearly multiple eigenvalues and for a basis of the corresponding invariant subspaces is described. The input matrix may be real or complex, dense or sparse. The method is based on a quadratically convergent Newton-like method; it includes the case of defective eigenvalues, uncertain input matrices and the generalized eigenvalue problem. Computational results show that verified bounds are still computed even if other eigenvalues or clusters are nearby the eigenvalues under consideration.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65G20 Algorithms with automatic result verification
65F50 Computational methods for sparse matrices
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